Mr Sim, of Seaforth Road, Aberdeen, collapsed and died in Dundee's Hindmarsh Avenue while walking back to his car following the match.
A spokeswoman for Tayside Police said: "There are no suspicious circumstances."
Tributes to Mr Sim were posted on an Aberdeen FC fans' web forum, including a message from his son, Barry, who wrote: "He was an Aberdeen man through and through. I think 'true fan' about sums him up. He lived and breathed his beloved Dons."