Sam Allardyce left Leeds by mutual consent on Friday after failing to save the club from relegation to the Championship in his four-game spell as interim boss.
Allardyce, 68, arrived at Elland Road to replace the sacked Javi Gracia as Leeds battled to extend their stay in the Premier League to a fourth successive season.
But Leeds lost three and drew one of their games under the former England boss, with their relegation sealed on the last day of the season.
Allardyce had hinted he would be willing to remain in charge next season to oversee Leeds' bid for a quick return to the top flight.
But, after talks between Allardyce and the club hierarchy on Thursday, Leeds have opted to move on from the former Newcastle, Everton and West Ham manager.
"Leeds United and Sam Allardyce can confirm that both parties have mutually agreed for Sam's spell at the club to end following the completion of the 2022-23 season," a Leeds statement said.
"Sam joined the Whites for the final four games of the campaign and despite spirited performances against Manchester City and Newcastle United, the objective of staying in the Premier League was not reached."
Leeds said they hoped to announce their new head coach "in the coming weeks".
- 'Long-term project' -
Allardyce had been out of football since suffering the first top-flight relegation of his managerial career with West Bromwich Albion in 2020-21.
He earned criticism for comparing himself to Manchester City manager Pep Guardiola and Liverpool boss Jurgen Klopp during his first press conference after taking over at Leeds.
With Leeds now set for at least a season in the second tier, it remains to be seen if Allardyce returns to the game or ends his long managerial career.
"It has been an honour to manage Leeds United, a great club with an incredible fan base, who deserve to be in the Premier League," Allardyce said.
"At this stage in my career I am not sure taking on this challenge, which is potentially a long-term project, is something I could commit to, but I wish the club every success for the future and hope the club returns to the Premier League, where they belong."
Allardyce arrived at Elland Road with Leeds sitting 17th in the table, outside the bottom three on goal difference.
Leeds lost his first game in charge at Manchester City and after a creditable 2-2 home draw against Newcastle, they surrendered their top-flight status with successive defeats to West Ham and Tottenham.
Relegation capped a dismal season for Leeds, who only turned to Allardyce in a desperate move after dismissing Gracia.
Gracia departed after only 10 weeks in charge having replaced the sacked Jesse Marsch in February.
Leeds chief executive Angus Kinnear added: "We thank Sam for being brave enough to step in and do all he could to save us.
"Sadly, it was not to be, but Sam, Karl (Robinson) and Robbie (Keane) did everything they could to lift the mood at Thorp Arch and Elland Road and for that we are all extremely grateful."
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