"I will always be very grateful to the club for giving me the opportunity to manage in the Premier League," said Zola, 43, in a statement.
West Ham replaced him with former Portsmouth boss Avram Grant on 3 June.
Zola took over at Upton Park following Alan Curbishley's resignation in September 2008, guiding the club to an impressive ninth place in the Premier League.
He signed a four-year deal with the Hammers in April 2009 reported to be worth £1.6m a year.
The former Chelsea favourite still had three years to run on that deal when he was sacked by West Ham owners David Sullivan and David Gold, who took over at the start of the year.
However, the ex-Italy striker has negotiated a settlement with the assistance of the League Managers' Association.
"I would like to offer my sincere thanks to all of the players, staff and fans who supported me so well during my time at the club and I wish them every success for the future," added Zola.
"I would also like to thank the LMA for their support and hard work during the difficult period of my contract termination process.
"I am looking forward to finding a new challenge in the game and returning to management as soon as possible."
A statement from West Ham read: "West Ham United would like to thank Gianfranco Zola for his efforts during his time at the club.
"We would like to thank both him and the LMA for their professionalism in reaching a satisfactory settlement and we wish Gianfranco well for the future."
Source: BBC Sport
Source: BBC Sport