The 25-year-old was a free agent this summer after being released by Rovers at the end of last season.
Goodwillie started his career with Dundee United, scoring 40 goals in 136 appearances in all competitions before leaving for the Premier League with Blackburn.
But he was never able to secure a regular place at Ewood Park after his first season, when he played 20 times, and he spent most of last season on loan, first back at Tannadice and then with Blackpool, where he scored three goals in 10 games.
Dons boss Derek McInnes said: "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."