"The board of directors would like to thank him for his contribution and wish him well for the future.
"The club will now be focusing its efforts on seeking a replacement.
"The club will be making no further comment on this matter."
Bookmakers have made Croatia coach and former West Ham defender Slaven Bilic, Portsmouth boss Avram Grant and former Manchester City coach Mark Hughes as favourites to fill the vacancy.
Zola's position with the Hammers was uncertain following the takeover by David Gold and David Sullivan in January 2010.
Sullivan, who previously part-owned Birmingham City with Gold, labelled Zola's team "pathetic" following the 3-1 defeat by Wolves.
And when asked about the Italian's future after the match, Sullivan responded: "I wouldn't like to comment on that - who knows?"
It then appeared Zola was ready to jump before being pushed following the loss to Stoke on 27 March - West Ham's sixth successive defeat.
"I will consider overnight whether I'm doing a good job for this club or not," he said after the match but then stated he was "determined to carry on" the following Monday.
But after all but securing the club's Premier League future with a 3-2 win over Wigan, Zola was dealt another blow by the board when he revealed he had not been consulted over a bid for West Brom midfielder Graham Dorrans or about Sullivan's announcement the entire squad was for sale except midfielder Scott Parker.
Zola, who began his playing career in 1984 for Italian side Nuorese, made his name at Napoli, helping the club to their second Serie A title in 1990.
He moved to Parma in 1993 and played in both legs of the 2-1 Uefa Cup final win over Juventus two years later.
Zola was then brought to Chelsea for £4.5m by manager Ruud Gullit in 1996.
His silky skills were much admired in the Premier League and he won the Football Writers' Association player of the year award in 1997.
He also added an FA Cup winner's medal to his collection when he helped the Blues to a 1-0 win over Aston Villa at Wembley in 2000.
Zola ended his playing career at Cagliari, helping the club to promotion to Serie A in 2004.
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