Peters, who helped England to win the World Cup in 1966, died at the age of 76, his former club, West Ham United announced on Saturday.
Peters scored in the final against West Germany when the Three Lions lifted the trophy.
A family statement
“It is with profound sadness that we announce that Martin passed away peacefully in his sleep at 4 a.m. on Saturday.
“A beloved husband, dad and grandad, and a kind, gentle and private man, we are devastated by his loss, but so very proud of all that he achieved and we are comforted by the many happy memories we shared.”
Peters joined West Ham in 1959 and was a key player in the side that won the 1965 Cup Winners’ Cup final at Wembley.
The midfielder won 70 England caps and scored 100 goals in 364 first team appearances for West Ham before moving across London to join Tottenham Hotspur in 1970 in a deal that saw striker Jimmy Greaves go the other way.