A boyhood supporter, he joined the Ibrox club from school in 1960 and made his debut just after his 18th birthday in November 1962 before going on to score 145 goals in 163 games over the next five years.
He won four major honours with Rangers including the League Championship in season 1963-64, the Scottish Cup in 1966 as well as two Scottish League Cups.
Other highlights include two goals in his first Old Firm appearance in 1963 aged just 18, four in the 1963 League Cup final win over Morton and both goals in the 1964 League Cup final victory over Celtic.
He left the club in 1967 to join Preston North End but returned to Scotland a year later to sign for Aberdeen, where he made 186 appearances, scoring 62 goals, and lifted the Scottish Cup in 1970.
Forrest also earned international recognition, winning five Scotland caps between 1965 and 1971. He ended his career at San Antonio Thunder, via spells in South Africa and Hong Kong.
A Rangers statement read: "The Rangers family is today saddened by the loss of former striker, Jim Forrest, at the age of 79.
"Forrest remains one of the most talented and natural finishers to don the famous blue jersey and has left an indelible mark in the club’s history. The thoughts of everyone at Rangers are with Jim’s family and friends."
Aberdeen also said they were "deeply saddened" by Forrest's passing, adding: "The thoughts of everyone at Pittodrie are with Jim's family and friends at this sad time."