The club said on Friday that Lambert left his position "as manager by mutual consent", reports Xinhua news agency.
"Whilst he was unable to guide us to Premier League safety after being appointed in January, it certainly wasn't due to a lack of effort, professionalism and dedication on his part," the statement added.
The club will appoint a replacement "as soon as possible" in order to give the new manager time to prepare for the challenge of the 2018/19 season in the Championship.
Stoke ended a decade in the Premier League with a 2-1 victory at Swansea on Sunday, but Lambert managed only two wins from his 15 games in charge.
Stoke, who were relegated to the Championship courtesy of their home defeat by Crystal Palace on May 5, collected 13 points under Lambert, who was given the task of trying to preserve the club's top-flight status after Mark Hughes was sacked in January.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
