Marco Silva is favourite to land the vacant manager's job at Crystal Palace after bringing his short spell at Hull to an end.
The relegated Tigers admitted defeat in their bid to keep hold of Silva, who made an impression after replacing Mike Phelan in January.
Following meetings with the club's owners on Wednesday, Silva opted to walk away and is already heavily favoured to replace Sam Allardyce at Selhurst Park.
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."
Silva's departure had been widely expected and he was strongly linked with Porto, but now appears more likely to remain in the Premier League.
The former Sporting Lisbon and Olympiacos boss made a big impression as he led the Tigers from a seemingly hopeless position in January to the brink of safety.
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 understand why he wants to stay in the Premier League or go to a big European club with the prospect of Champions League football."
Hull are now searching for their fourth manager in less than 12 months following the departures of Steve Bruce, Phelan and Silva.