The man, who was in his 50s, was taken from the stadium to the Southern General Hospital in Glasgow at around 3.30pm on Saturday but later died.
A spokesman for Strathclyde Police said: "A post mortem exam will take place in due course to establish the exact cause of death, however there are no suspicious circumstances."
Rangers defeated Berwick Rangers 4-2 in front of almost 45,000 fans and after the match goalscorer David Templeton tweeted: "So sad to hear about the fan who passed away at the game. Thoughts go out to the family and friends."




