West, who also had spells at Blackpool and Tranmere, had been battling a long illness and passed away peacefully on Sunday.
West helped the side to the First Division title in 1963 and 1970 as well as the FA Cup in 1966.
After becoming Harry Catterick's first signing from Blackpool in 1962 for £27,000 - a then-record fee for a goalkeeper - West went on to make 402 appearances and was capped three times by England.
He retired from football in 1973 only to make a comeback three years later with Tranmere.
When he hung up the gloves three years later, West went into security, working at RAF Woodvale in Southport before retiring.
Fellow Everton favourite Graeme Sharp told the club's official website upon hearing of West's passing: "It's dreadfully sad. I met Gordon many times and he was a real larger-than-life character who loved Everton.
"All Evertonians will be distressed at this news and my thoughts are with his family."