Allardyce, 68, could not save Leeds from relegation after being appointed in a last-ditch bid to keep them in the Premier League with four games of the season remaining.
A club statement read: "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.
"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."
Allardyce had been well known for helping clubs survive relegation - with Albion turning to him back in 2021 after the dismissal of Slaven Bilic.
However, following just four wins in 26 games, Albion couldn't avoid the drop and after talks over is future he left the club shortly after the conclusion of the campaign.
And that has been a similar situation at Elland Road - with Allardyce leaving after earning just one point in four games.