Yes from my understanding it was Goebbels idea, as the propaganda minster he wanted to portray Germany as a modern & friendly nation as well as the belief that Hitler tried to ingrain that the forerunners of his beloved "Aryan race" where from Ancient Greece. This was the first instance in the modern Olympics, yes after the inclusion of the torch (not a relay) in the 1928 Olympics. It was devised by German sports official, Carl Diem. Hitler is rumoured to have said this:

The sportive, knightly battle awakens the best human characteristics. It doesn't separate, but unites the combatants in understanding and respect. It also helps to connect the countries in the spirit of peace. That's why the Olympic Flame should never die.

This really does show that Hitler would do anything to keep the "happy-go lucky" façade & fool the west into thinking everything was fine. Leni Riefenstahl, a German filmmaker whom Hitler admired was commissioned to document the games & so he did. In 1938, Riefenstahl's Olympia was released. It is known as being a prime example of Nazi propaganda.

I'm going to expand a little on some of the goings-on in Germany at the time & the links to the other countries competing & the games' image. Historian, Susan D. Bachrach states that Hitler was using this Olympics to paint an image of a resurgent Germany (this includes things like rearmament (even though we didn't know about this at the time), he showed this resurgence by trying to portray his Aryan German athletes as superior to the African-American athletes that were also competing. Jesse Owens is a good example of Hitler's plan failing, Because Owens won 4 gold medals. Hitler certainly wasn't a happy bunny at all, In the first day of thev competition, Hitler only shook hands with the German victors however Olympic committee officials gave Hitler the choice of shaking all the victors hands or none at all. Unsurprisingly the stubborn dictator chose the latter.

Owens had this to say on Hitler & the whole medal ceremony affair:

Hitler had a certain time to come to the stadium and a certain time to leave. It happened he had to leave before the victory ceremony after the 100 meters. But before he left I was on my way to a broadcast and passed near his box. He waved at me and I waved back. I think it was bad taste to criticize the 'man of the hour' in another country.

Albert Speer, German "Architect of The Third Reich" said this about the attitude & relationship between Hitler, Owens & the medal ceremony affair:

Hitler "was highly annoyed by the series of triumphs by the marvelous colored American runner, Jesse Owens. People whose antecedents came from the jungle were primitive, Hitler said with a shrug; their physiques were stronger than those of civilized whites and hence should be excluded from future games.

Further Reading:

1. Richard Evans' The Third Reich in Power: 1933-1939 The second book in his 3rd Reich trilogy (2005)

2. Christopher Hilton's Hitler's Olympics: The 1936 Berlin Olympic Games (2006)

3. Susan D. Bachrach's The Nazi Olympics: Berlin 1936 (2000)

4. Guy Walters' Berlin Games: How Hitler Stole the Olympic Dream (2006)

5. Jeremy Schaap's Triumph: The Untold Story of Jesse Owens and Hitler's Olympics (2008)

P.S. This is only a quick response, If you have any more questions feel free to ask them, then I'd be more than happy to try & answer them :)

EDIT: I've expanded a little about Jesse Owens experience in the Games & how Hitler felt about it