The 19-year-old’s deal at London Stadium expires on 30 June
Right-back Pablo Zabaleta and midfielder Carlos Sanchez will also leave when their deals expire at the end of this month.
Ngakia had received an offer with improved terms on his existing deal but declined the deal, with the 19-year-old seeking a new challenge.
He has made five first-team starts since David Moyes returned to the club in December, the most recent of which came against Wolves in the first game after the break in the season caused by the coronavirus pandemic.
West Ham had hoped to convince him to remain at the club but Ngakia, who came through the West Ham youth system, will now leave on Tuesday, 30 June.
In a statement, West Ham said: “In line with our structure and policy, Ngakia was offered significantly improved terms to reward his breakthrough into the first-team squad this year, along with further contractual enhancements linked to his future progress and success.
“However, the player and his representatives declined to accept any of the offers, and also turned down a short-term extension until the end of the current season.”
Zabaleta, meanwhile, was unable to extend his deal until the end of the season, due to an injury.
He joined the Irons on a free transfer from Manchester City in 2017, linking up with his former boss at Etihad Stadium, Manuel Pellegrini.
The Argentine made 80 appearances in claret and blue, and scored his only goal in the FA Cup win over Gillingham earlier this season.
Sanchez joined the same summer as Zabaleta, but only played 18 times over the past two seasons, after suffering a serious knee injury during his first season at London Stadium.
West Ham added: “The club would like to thank Pablo, Carlos and Jeremy for their service and wish them well in their future careers.”
Tags: Football, West Ham United
