Antonio joined West Ham from Nottingham Forest for an undisclosed fee, reported to be £7m, in 2015.
He is the club's record Premier League goalscorer, scoring 68 goals in 268 top-flight appearances.
Meanwhile, France international Kurt Zouma, 30, who joined the the club four years ago and is on loan at Al-Orobah FC in the Saudi Pro League, will leave West Ham at the end of the month.
The club announced last month that defenders Aaron Cresswell and Vladimir Coufal, goalkeeper Lukasz Fabianski and striker Danny Ings will leave when their contracts expire this summer.