The 48-year-old held talks with vice-chairman John Coates on Friday and it was decided that both parties would go their separate ways.
Stoke dropped out of the top flight following a 10-year stay, with Lambert winning just two of his 15 games in charge - one of those coming on the final day after relegation had already been confirmed.
A statement on the Potters' official website read: "The club would like to thank Paul for his work over the past four months and wish him well for the future. 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.
"Paul would like to thank the board, players and staff for the opportunity and their support. He would also like to thank the fans for their unwavering support. Whilst looking forward to his next challenge, he would like to wish the club every success next season.
"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."
Lambert, who replaced Mark Hughes at the bet365 Stadium, has previously spent time in charge of Norwich City, Aston Villa and Wolverhampton Wanderers.