"It's not often you get the opportunity to watch a penalty shootout between an English team and a German team and watch the English team win," Cameron told reporters in Chicago before a NATO summit.
"There are many great privileges in this job but to be able to do that with the German chancellor was a great moment - but we did hug and make up afterwards," he said.
Cameron was photographed with his arms thrust aloft in triumph while watching Saturday's final on television with other world leaders during a break in the Group of Eight summit at the U.S. presidential retreat at Camp David, Maryland, on Saturday.
In the photo Cameron was next to U.S. President Barack Obama, with his mouth open in amazement, and Merkel, who looked disappointed.
Chelsea became the European champion when Didier Drogba made the last kick of the shootout in Germany after the match ended in a 1-1 stalemate after extra time.
It was sweet revenge for Cameron after he and Merkel watched part of Germany's 4-1 thrashing of England at the 2010 World Cup on television at a Group of 20 summit in Toronto.
Cameron said he had to explain some of the finer points of Saturday's penalty shootout to Obama "and he was beginning to catch up on the rules by the time it was over."
"You've got the American president not fully understanding the rules of football, or soccer as he would call it, a very despondent German chancellor and, of course, another happy man in the room, which was the Russian prime minister [Dmitry Medvedev]," he said.
Chelsea's success was built on the millions invested in the club in the past nine years by Russian billionaire Roman Abramovich.
Cameron said the leaders had watched a bit of the game and then he had insisted they get back to their discussion of weighty global matters, including the euro zone debt crisis.
"I got everyone back in the room but when the penalty shootout started Angela Merkel drifted away and after trying to focus minds on what we were talking about I drifted away too, obviously suspecting that an England-Germany penalty shootout was going to be another difficult night for me," he said.
"That is why you see me being quite so elated when Drogba put that great penalty in," he said.
