The probe will be an additional dimension of an investigation into the response of government-owned agency Northern Ireland Water, which will be conducted by the region's Utility Regulator.
The minister's department is responsible for NIW and he has been heavily criticised for its handling of the emergency which culminated in the resignation of NIW's chief executive Laurence MacKenzie on Wednesday.
At the height of the crisis more than 40,000 homes and businesses were left without water.
It was triggered after a period of deep freeze over Christmas ended with a rapid thaw, leading to thousands of burst water pipes.
But the focus of the criticism of NIW was in regard to its failure to communicate adequately with customers, many of whom were left with no water for two weeks.
The Executive agreed to commission the two experts because Utility Regulator Shane Lynch's statutory responsibility does not extend to Mr Murphy's regional development department.
One will be appointed by Democratic Unionist First Minister Peter Robinson and the other by Sinn Fein Deputy First Minister Martin McGuinness.
Their work will be added to the findings of the regulator to form one over-arching report, which is due to be published next month.
The remit of the investigation was agreed after a marathon six and a half hour Executive meeting at Stormont Castle in Belfast.
At its close, Mr Robinson said the investigation would be in two parts.
"The regulator will carry out an investigation into matters relating to Northern Ireland Water but it is very clear that there are matters beyond that where there is public concern and we want to ensure that those matters are investigated and those relate to the role of the department, the role of the minister and some other issues where the regulator might be conflicted," he said.
"So it is very clear that we needed to have something more than the regulator looking at this issue."
Mr Murphy, who has faced calls to follow Mr MacKenzie's lead in resigning, expressed confidence the probe would find no issue with his performance.
"I am quite confident about my own role in all of this," said the Sinn Fein MLA outside Stormont Castle.
"I am actually confident that I probably over-extended my role by going directly to NIW in terms of their response and insisting that they operationally up their game in response to this.
"But I am quite content for any investigation to look into that and I will respond to it when it reports."
After claims Mr MacKenzie may be in line for a major severance pay-off, Mr Murphy again insisted he wanted to ensure the under-fire official received only his minimum contractual entitlement and that the payout amount was made public.
Earlier, a Stormont committee was told NIW was overwhelmed by more than a million contacts from the public at the height of the crisis.
Officials from the government-owned company received 600,000 phone calls in three days at the height of the episode and was sent 10,000 emails, while its website was bombarded by half a million hits.
But Mr MacKenzie, who is set to officially leave office today, was slammed for failing to meet the committee over his organisation's handling of the emergency.
Chairman of the Regional Development Committee Fred Cobain said Mr MacKenzie had a duty to account for his company's actions.
"I have to say the committee is deeply disappointed that we don't have the chief executive here, who is still the chief executive of Northern Ireland Water," said Mr Cobain.
"He should have been here. This is a huge issue, not just for this committee and the Assembly, but for the thousands of people who have suffered. He has a responsibility to those people.
"As far as we are concerned he should have been and he is not."
The NIW officials who met the committee apologised for Mr MacKenzie's absence and said he was involved in finalising the details of his resignation.
The man set to take over as acting chief executive, Trevor Haslett, said his company was swamped by the events around Christmas and had to deal with unprecedented circumstances.
But he added: "On behalf of Northern Ireland Water can I first apologise to all of our customers who were inconvenienced, seriously inconvenienced over a lengthy period.
"I don't think anyone at Northern Ireland Water, the board, the executive team, is happy about that."
One of Mr Murphy's arch critics, the SDLP's Conall McDevitt, gave a guarded welcome to the investigation's added dimension.
"The SDLP welcome the Executive's acknowledgement that a separate independent investigation into Conor Murphy's conduct is needed," he said.
But Mr McDevitt said he would reserve judgment on the integrity of the investigation until the names of the two independent experts were revealed.
HOW WATER PIPES CRISIS UNFOLDED
The head of the Northern Ireland Water (NIW) company has stepped down after tens of thousands of families were left without water following a rupture in the region's water supply system brought on by the recent cold snap.
Here are how events unfolded:
December 23: NIW announced it was to invest more than £577 million in its pipes and other equipment over the next three years as part of wider efforts to upgrade its antiquated infrastructure for drinking water and waste water. Ministers at the Northern Ireland Assembly had only days before a draft budget was unveiled which ruled out introducing water charges to fund an upgrade. NIW also reminded people to lag pipes and keep heating on to avoid leaks in cold weather.
December 26: After arctic weather conditions saw temperatures plummet to record lows of -20C, NIW reported it was dealing with large numbers of burst pipes as the big freeze gave way to the big thaw. NIW said it had received over 14,000 calls in the previous five days. Extra call handlers were said to have been brought in. A spokesman said: "Our teams are on site and working as quickly as possible to repair these bursts and restore water supply to customers."
December 27: It emerged 4,000 houses in the Coalisland area of Co Tyrone were without water after a pipe connected to the Lisnastrane reservoir ruptured. Water supplies were also hit in parts of Belfast, Armagh, Newry, Bessbrook, Cullyhanna, Dromore, Keady and Craigavon. NIW said many leaks were thought to be inside private properties and, therefore, outside their responsibility.
December 28: The problem escalated with even greater numbers of homes without water supply. NIW came under fire for failing to cope with the deluge of calls for information from householders. Deputy First Minister Martin McGuinness and regional development minister Conor Murphy visited homes flooded by sewage in Lurgan, Co Armagh, when drains overflowed. On the wider front, water levels were said to be low in reservoirs and NIW moved to shut down supply to some areas amid the battle to fix leaks.
December 29: The chief executive of NIW Laurence MacKenzie faced calls to resign as tens of thousands of homes were hit by water loss. As crisis developed, 160,000 litres of emergency supplies of bottled water were shipped from Scotland. Families complained of days spent without adequate toilet or washing facilities. Mr MacKenzie faced the media, but said his immediate focus was to get all customers back on supply. The Stormont Executive confirmed plans to meet the next day to discuss the growing crisis.
December 30: First Minister Peter Robinson and deputy First Minister Martin McGuinness emerged from the Executive meeting and attacked NIW's performance. Mr Robinson said the episode was "shambolic", Mr McGuinness said there "has to be accountability" after NIW "miserably failed our citizens". Mr Murphy, who was also under growing political pressure, said the Executive backed an independent review but wanted supplies restored as an urgent priority. It was confirmed that around 6,000 customers had no water since December 27. A further 3,500 to 60,000 had interrupted supplies for up to eight hours as they were rotated between areas. NIW increased the supply of water to customers to the highest level ever, increasing from 600 million litres per day to 860 million litres per day. The increase in demand was said to be largely because of leakage from bursts on private properties. On one property, NIW located a burst pipe which was draining 2.5 million litres from the system, the equivalent of the water supply for between 2,000 and 3,000 homes. Other major leaks were later detected on private property.
December 31: After a special three-hour meeting of the NIW board, its interim chairman Padraic White conceded the company's emergency plan had failed to deal with the unprecedented crisis. He said Mr MacKenzie had not resigned and said NIW was to redouble efforts to tackle problems and would ramp-up its communication with the public. The board accepted the call for an independent review of the episode. Conor Murphy was briefed by Mr White. The minister later said the terms of reference for an independent probe would be agreed within days, but the priority was fixing leaks and not securing "heads on a plate". The Irish Republic's Louth Council announced it was to deliver at least 100,000 litres of drinking water by tanker to the Newry area on the northern side of the Irish border as part of a rolling process of assistance. Scotland promised to send further supplies of bottled water.
January 1: NIW faced into the worst New Year it could have imagined. There were persistent political calls for resignations at the company and major criticism of minister Murphy. Around 2,600 homes were still without any supply. Water was still pouring out of leaks in the system and the under-fire Government-owned utility had to extend its on/off rotation system to other homes in order to replenish reservoirs. But while 500 NIW staff battled to restore supplies to the region's crippled system, vandals were blamed for emptying out almost 5,000 gallons of water from temporary tanks in one of the badly hit areas in Coalisland, Co Tyrone.
January 2: The number of houses without water was down to around 800, but the political furore showed no sign of abating. Water supplies were cut to around 45,000 properties overnight. Meanwhile education chiefs expressed hopes that relatively few schools would be closed because of leaks.
January 3: NIW said 300 customers had yet to be reconnected to running water. Supplies to around 10,000 properties were still disrupted. The areas included greater Belfast where service reservoirs had yet to fill up. Meanwhile a police helicopter and postal staff were asked to help get the remaining customers back on supply. The helicopter, fitted with thermal imaging technology, was being used to check trunk mains in remote areas. At the same time, the Post Office agreed its postmen and women would report any leakage they spotted on their rounds. NIW was accused of failing to seek help from colleagues in Britain quickly enough, while political parties continued their pressure on Sinn Fein's Conor Murphy, but his party accused opponents of merely seeking to score political points.
January 4: NIW board met again. The company later denied its Chief Executive was set to resign. It was widely believed, however, that he was poised to step down.
January 5: NIW said it had reconnected all the homes that had lost water during the crisis. The company's figurehead Mr MacKenzie subsequently fell on his sword and resigned from his post.