Ray Dunning, 42, collapsed as he watched his team lose 1-0 to the league champions at the King Power stadium - a result that saw Rovers relegated.
According to reports, attempts were made to save his life in the stands before he was taken to hospital.
In a statement, the club said: "Doncaster Rovers would like to express our deepest sympathies and condolences to the family and friends of Ray Dunning, the Doncaster Rovers supporter who, it has been confirmed, died on Saturday.
"An avid follower over the years, Ray was taken ill whilst attending the Sky Bet Championship fixture between Leicester City and Doncaster Rovers at the King Power Stadium, Leicester, on May 3, 2014.
"The thoughts of everyone at the club are with his family, who have sent their thanks to the Doncaster Rovers fans for their efforts inside the stadium and the messages of support they have received."