The Mariners said Friday that Wedge will manage the final three games of the season against Oakland.
"I accept Eric's decision not to return and thank him for his hard work here the past three years. I want to wish him and his family all the best in the future," general manager Jack Zduriencik said in a statement released by the team.
Wedge was brought in to replace Don Wakamatsu - who was fired during the 2010 season - because of the track record he built in Cleveland taking the Indians through a rebuilding process and nearly leading them to the World Series.
But the rebuilding never seemed to end in Seattle with a constant influx of young prospects from the minors being called up and some veterans failing to meet expectations.
Seattle, which has never reached the World Series, entered the final weekend 70-89, assured of its fourth straight losing season.
Wedge complained this week that he felt he was left "hanging out there" by the organization on his status for 2014.
"But I'm coming here and doing my job," Wedge had said Wednesday. "You know how passionate I am about this team, and these players in particular, and this organization. The unfortunate part about how it's being handled is the effect it has on the players. That's why we're all here, is for the players."
Seattle was on the fringes of contention in July, winning eight straight games, when Wedge suffered a minor stroke.
He was helped off the field during batting practice on July 22 and was rushed to a hospital. He was diagnosed with a mild stroke the next day and began a monthlong recovery process that called for changes in his diet, exercise and dealing with the stress of his occupation. Robby Thompson filled in while Wedge was out.