The 25-year-old former Dundee United player was freed by Blackburn Rovers this summer.
Goodwillie has been capped three times by Scotland and moved to Rovers in 2011 for around £2m.
Derek McInnes was thrilled to add the proven goalscorer to his squad. "I'm delighted to have secured the signature of David. He's a striker who has a real capability and it's up to us as a staff and him as a player to get the very best from him.
"He joins a squad of good players and he wants to be part of a successful season here at Pittodrie."