However the 35-year-old has been offered a contract extension.
Foster, who made his debut for the county in 2000, became vice-captain in 2007 before taking over from Mark Pettini in 2010.
"The club would like to thank James for his service as captain and look forward to him being a major part of Essex's future," a club statement said.
Foster skippered Essex in all 16 of their County Championship games last season and led them to third place in Division Two, while Ryan ten Doeschate captained the one-day and Twenty20 sides.
The county, who appointed former England bowler Chris Silverwood as their new head coach earlier this month, said they would be looking at the captaincy options in the new year.
Essex have announced James Foster is no longer their club captain after five years leading the Division Two side.