Finch will replace veteran wicketkeeper-batsman Kumar Sangakkara while the former Sri Lanka skipper is away at the Caribbean Premier League, due to start in July.
The 29-year-old opener is currently one of the most destructive batsmen in the world. He is currently second on the T20 international batting rankings, which is headed by India's Virat Kohli.
His signature comes after Surrey earlier announced that West Indies all-rounder Dwayne Bravo would join them for the next season.
Finch will be available to play in all three formats and has first division experience having spent the past two seasons at county champions Yorkshire.
"This is a great opportunity for me and one I am very much looking forward to," Finch was quoted as saying by ecb.co.uk.
"To have the chance to play all forms of the game is a challenge I will relish, as I have ambitions to represent Australia in Test match cricket. I'm aware that Surrey have an exciting young squad and I hope I am able to add to their obvious talent," he said.
Surrey director of cricket Alec Stewart added: "Securing a player of Aaron's quality for such a busy period of red and white ball cricket is excellent news for the club and I'm confident we will see his qualities in all formats of the game."