Detectives from Legacy Investigation Branch said the suspect is being interviewed at a police station in Belfast.
Thirteen people were killed on January 30 1972 by members of the Parachute Regiment when British paratroopers opened fire on a civil rights march in Londonderry.
Another victim of the shootings died months later.
It is understood the pensioner was arrested on suspicion of the murders of William Nash, 19, John Young, 17, and Michael McDaid, 20, all of whom were shot dead in close proximity to one another at a rubble barricade on Rossville Street.
It is believed the former soldier is also being questioned about the attempted murder of William Nash's father Alexander. Mr Nash came to the barrier to save his son but was shot in the arm and body.
It is understood the soldier gave evidence to the Government-commissioned inquiry into Bloody Sunday, undertaken by Lord Saville, under the cipher Lance Corporal J.
Kate Nash, William's sister, welcomed the development.
"We have always fought very hard to be treated equally within the justice system," she said.
The officer leading the investigation, Detective Chief Inspector Ian Harrison, said today’s arrest marked a new phase in the overall investigation which would continue for some time.
The man would have been 23 at the time.
This is the first arrest since the murder investigation was launched into the Bloody Sunday events in 2012.
The investigation came following the Government- commissioned inquiry led by Lord Saville which found that none of the victims were posing a threat to soldiers when they were shot.
<< scroll down for key findings of Lord Saville's report >>
The inquiry took 12 years to complete.
Prime Minister David Cameron apologised for the Army's actions following the publication of the report in 2010.
He branded them "unjustified and unjustifiable" and said he was "deeply sorry".
In September, the PSNI announced their intention to interview seven former soldiers about their involvement on the day.
Mickey McKinney, whose brother William McKinney was one of those killed, also welcomed the arrest.
"We are hopeful this is the start now of bringing in suspects to be questioned," he said.
"Our quest for justice goes on. We are not going to stop until the people responsible for the murders are in court and sentenced."
Also welcoming the arrest was Sinn Fein MLA Raymond McCartney who described the arrest as a "step forward in the long campaign for justice.
He said: "I would call on the PSNI to ensure the relatives are kept up to date of all developments on the investigations.
"Sinn Féin will continue to support the Bloody Sunday families in the campaign for truth and justice."
Key findings of Lord Saville's report into Bloody Sunday
Lord Saville exonerated the victims of Bloody Sunday and delivered a damning account of the conduct of soldiers, concluding they had fired more than 100 rifle rounds on civil rights demonstrators without justification.
The Saville report's key findings were:
''The firing by soldiers of 1 Para caused the deaths of 13 people and injury to a similar number, none of whom was posing a threat of causing death or serious injury.'' This also applied to the 14th victim, who died later from injuries. The report added: ''We found no instances where it appeared to us that soldiers either were or might have been justified in firing."
''Despite the contrary evidence given by soldiers, we have concluded that none of them fired in response to attacks or threatened attacks by nail or petrol bombers.'' The report added that no one threw, or threatened to throw, nail or petrol bombs at soldiers.
The explanations given by soldiers were rejected, with a number said to have ''knowingly put forward false accounts''.
Members of the so-called Official IRA fired a shot at troops, but missed their target, though crucially it was concluded it was the paratroopers who shot first on Bloody Sunday.
The report recounts how some soldiers had their weapons cocked in contravention of guidelines, and that no warnings were issued by paratroopers who opened fire.
Speculation that unknown IRA gunmen had been wounded or killed by troops, and their bodies spirited away, was dismissed. There was no evidence to support it, and it would surely have come to light, the report said.
Northern Ireland Deputy First Minister Martin McGuinness, second in command of the Provisional IRA in Derry in 1972, was ''probably armed with a Thompson submachine gun'' at one point in the day, and though it is possible he fired the weapon, the report said that cannot be proved. But Lord Saville concluded: ''He did not engage in any activity that provided any of the soldiers with any justification for opening fire.''
Lord Saville concluded the commander of land forces in Northern Ireland, Major General Robert Ford, would have been aware that the Parachute Regiment had a reputation for using excessive force. But he would not have believed there was a risk of paratroopers firing unjustifiably.
The commanding officer of the paratroopers, Lieutenant Colonel Derek Wilford, disobeyed an order from a superior officer not to enter troops into the nationalist Bogside estate; while Lord Saville found his superior, Brigadier Patrick MacLellan, held no blame for the shootings since if he had known what Col Wilford was intending, he might well have called it off.
No blame was placed on the organisers of the march, the Northern Ireland Civil Rights Association.
Neither the UK nor Northern Ireland governments planned or foresaw the use of unnecessary lethal force.