Cleese received the award ahead of a screening of "A Fish Called Wanda".
The festival's director, Mirsad Purivatra, said Cleese was someone who had taught all viewers the true meaning of humour. "We are presenting this Heart to someone who taught us to laugh at ourselves, that humour and irony can save lives, and we in Sarajevo know that very well."
Cleese said he was delighted to be in Sarajevo and that he already accepted the invitation to sit on the festival's jury next year. This is a time in history when perhaps we need comedians the most, he said.
He recalled the four-year siege of Sarajevo in the 1990s, saying he was deeply affected as well as touched by the fact that Sarajevo Film Festival was launched during the war. I hope you are all proud of that, he added.
The festival closes on Thursday.