Clarke leaves the club following Avram Grant's appointment as Zola's successor.
Zola was sacked after the end of the season despite keeping the Hammers in the Premier League and Clarke has now joined his former Chelsea team-mate in moving on.
Clarke told the club's official website: "I have enjoyed my time at West Ham. I was looking for a fresh challenge in football before I arrived and certainly got that.
"It was a good experience which will help me in the future. I would particularly like to thank the fans for all their support and the players and staff for their efforts.
"I will follow the club's progress with interest and I am sure, with the new stability off the pitch, that the team will have every opportunity to do well next season."
Source: Team Talk
Source: Team Talk