The Glasgow-born businessman, who became managing director of a major retail and betting company, was awarded the CBE in 1982 before later receiving a knighthood.
Carter joined the board of directors at Goodison Park in 1977 and replaced Sir John Moores as chairman two years later.
During his time as chairman Everton won the FA Cup, European Cup Winners’ Cup and were English champions on two occasions.
Carter vacated his position when Peter Johnson purchased Everton in 1994, but returned to his role after Bill Kenwright took over the club four years later.
A statement on the club’s official website read: “Everton Football Club is deeply saddened to announce that Sir Philip Carter has passed away.
“Sir Philip died peacefully at home on Thursday morning after a short illness.
“He served Everton with immense distinction over three spells and a full tribute will appear shortly.
“At this time it would be appreciated if everyone can please respect the family’s wish for privacy.”