Gilzean was diagnosed with a brain tumour towards the end of June, and it has now been confirmed that the 22-time Scotland international has died after battling the illness.
Gilzean played over 400 times for Tottenham, and scored 133 goals in a 10-year spell with the London club.
The former striker started his professional career with Dundee, however, and was a prolific scorer for the Scottish outfit before making the move to Tottenham in 1964.
Everyone at the Club is deeply saddened to learn of the passing of our legendary former striker Alan Gilzean. Our thoughts are with his family and friends at this extremely difficult time. pic.twitter.com/uECwQ5mPUf— Tottenham Hotspur (@SpursOfficial) July 8, 2018
In 2009, Gilzean was inducted into the Scottish Football Hall of Fame.