Ladybank-born Martin moved to Ibrox in 1958 from Hamilton, initially as a third-choice keeper to George Niven and Billy Ritchie, and during his 12 years at Ibrox he made 126 appearances.
During the 1966/67 season he wore the No 1 jersey in the Cup Winners' Cup, playing against Borussia Dortmund, Real Zaragoza, Slavia Sofia and in the final which Rangers lost 1-0 to Bayern Munich.
Former team-mate Sandy Jardine has fond memories of the tall shotstopper and told the Rangers website: "Norrie was at Rangers for a long time and he was a really nice lad.
"He will be remembered for being part of the team that reached the European Cup Winners' Cup Final in 1967 but he made over 100 appearances for the club.
"Had it not been for injuries and having to compete with the likes of Billy Ritchie he would have undoubtedly made a lot more. It was very sad to hear that he had passed away after a short illness."