He had netted for England in their 1966 World Cup final win over West Germany.
West Ham said as quoted by the BBC: "The 1966 World Cup winner passed away peacefully" on Saturday after "a long and courageous battle with illness".
"He is the fifth member of English football's greatest-ever team now sadly lost along with Alan Ball, Ray Wilson, Gordon Banks and his fellow West Ham Academy hero and great friend, Bobby Moore," the club added.
His former England teammate Sir Geoff Hurst was quoted as saying by the BBC: "Martin Peters was one of the all-time greats and a close friend and colleague of mine for in excess of 50 years.
"A fellow World Cup final goalscorer and my West Ham partner for years along with Bobby Moore. RIP old friend."
Sir Bobby Charlton, who also played alongside Peters in 1966 said: "We shared one of the greatest days of our lives at Wembley and the fact Martin is one of only two Englishman to have scored in a World Cup final gives him a special place in England's history of the game.
"He was a fantastic footballer. As a teammate he was someone I could trust completely to do his job and I am proud to have shared that great day with him."
Peters joined West Ham aged 15 and played for them for 11 years before moving to Tottenham Hotspur in 1970.
( With inputs from IANS )