In William Shirer's account, Hitler believed that Roosevelt dying was the turning point of the war. The US would exit the war, and Russia and Britain would sue for peace. For him, the event was what could be called devine intervention.

He was of course not seeing things clearly at the time. Even if the US would have quit at that point, Germany was finished. But then again, if Hitler were to have been realistic, he probably wouldn't have ended up in that situation in the first place.

Anthony Beevor writes in "The Second World War" that Goebbels was very happy and immediately called to gongratulate his Fuhrer on Roosevelt's death to cheer Hitler up.