Hull have announced the departure of head coach Marco Silva.
The 39-year-old opted to leave his position following a meeting with the club's owners on Wednesday night.
Silva signed a short-term deal in January but failed to stave off the club's immediate return to the Sky Bet Championship.
Hull said in a statement: " The Club can announce that Marco Silva has opted to leave his position as Head Coach. Confirmation had been delayed due to finalising the terms of his release.
" Marco was offered the opportunity to continue the work he has done in the four-and-a-half months he has been at the KCOM Stadium. Unfortunately, after considering his future, he has chosen to leave in order to further his career and departs along with Assistant Head Coach Joao Pedro Sousa, First Team Coach Goncalo Pedro and Goalkeeping Coach Hugo Oliveira.
"Although disappointed by Marco's departure, we would once again like to place on record our appreciation of his efforts and those of his support staff. Despite only being in charge for a short period of time, the 39-yearold became a firm fans' favourite and will be forever remembered for his efforts to maintain our Premier League status.
"The Club will now undertake a thorough and considered recruitment process to appoint a replacement."
Tigers vice-chairman Ehab Allam told Sky Sports News: "The way the contract was structured meant there would be one year left on his contract had we stayed in the Premier League - but with relegation unfortunately he had the option to go.
"He's been fantastic for us but I accept he's a better calibre manager than the Championship. I u nderstand why he wants to stay in the Premier League or go to a big European club with the prospect of Champions League football.
"We'd love him to stay. We're very sad to lose him but I respect why he's taken the decision.
"We attained 21 points in 18 games (with Silva in charge) and if we'd had that through the (whole) season we'd have been mid-table.
"I can understand why there's so much interest in him. The improvement was there for all to see and if he gets a full season anywhere else I'm sure he'll do a fantastic job."
Silva's departure had been widely expected and he was strongly linked with Porto, while he also heads the betting to replace Sam Allardyce at Crystal Palace.
The news is a bitter blow to Tigers' fans, who made it clear they wanted him to stay during and after Sunday's 7-1 rout by Tottenham at the KCOM Stadium.
Silva's appointment was widely questioned when he replaced the sacked Mike Phelan in January with the Tigers seemingly doomed to the drop.
But the the former Sporting Lisbon and Olympiacos boss led the club to the brink of safety after a run of six wins from seven unbeaten home games in April.
Victory against Watford at the KCOM on April 22 extended his unbeaten home record as manager at four different clubs to 41 games.
But that run was halted at the worst possible time in their next game at the KCOM by already-relegated Sunderland and the Tigers went on to concede 11 goals in their last two matches.
Hull are now set to be in the hunt for their fourth manager in less than 12 months following the departures of Steve Bruce, Phelan and Silva.