Every piece of it looted from Jewish art collectors, according to The Guardian. By the Nazis of course.
Check out the Daily Mail for an even more lurid rendering of the same story. The DM adds a little more zempf to the story by telling us that many of the paintings were picked up at extortionately low prices from Jewish collectors desperate to flee Germany in the '30s.
While the papers spin a lovely yarn, there are a couple of things you might want to keep in mind. While this may well be a billion dollar/pound/euro collection today, it was something altogether different circa WWII. Picasso sketches traded for a few hundred dollars in the 1930's. Five number prices for most of these paintings didn't happen until twenty years after the war, and the multi-million dollar prices that this story is premised on took another generation to achieve.
There's also no effort in either story to give a cogent explanation as to how all this art, allegedly stolen by Nazis from Jewish collectors and dealers, ended up in the possession of Cornelius Gurlitt, the son of a Jewish art dealer.