The 68-year-old took charge of the Whites for their final four matches, but couldn't inspire the Yorkshire outfit to safety.
A 4-1 defeat to Tottenham at Elland Road on the final day of the season condemned Leeds to the Championship.
A club statement stated that it was a 'mutual' decision, with Allardyce only agreeing a short-term deal when he succeeded Javi Gracia.
Allardyce said: "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.
"I have really enjoyed working with the staff and players at the club and I would like to thank Angus Kinnear for the opportunity.
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"I'd also like to highlight the outstanding work of Karl Robinson and Robbie Keane who have worked tirelessly over the past few weeks.
"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."
Leeds CEO Angus Kinnear added: "We thank Sam for being brave enough to step in and do all he could to save us.
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"Sadly, it was not to be, but Sam, Karl and Robbie did everything they could to lift the mood at Thorp Arch and Elland Road and for that we are all extremely grateful."
Leeds have also announced that they will be appointing their next head coach in the coming weeks.
Allardyce's Leeds exit is not unexpected, with it reported on Thursday that he was set to leave following talks with Kinnear.
As it stands, Steven Gerrard is currently the bookies' favourite, with Brendan Rodgers and former Leeds midfielder Lee Bowyer among the other frontrunners.
Manchester United legend Roy Keane had declared that Allardyce would depart Leeds, as his 'ego' wouldn't let him manage in the Championship.
It led the former England boss to bite back, where he pointed out he coached Bolton and West Ham in the second-tier of English football.