The 21-year-old scored 12 goals last season, leapfrogging Darren Bent in the pecking order at Villa Park and breaking into the Austria team.
Weimann, who has progressed through the club's academy having moved from Rapid Vienna as a 15-year-old, showed his potential during a loan spell with Watford during the 2010-11 season and scored his first senior goals for Villa at the end of the following campaign.
"I'm really happy that I've signed. I love the club and it's been brilliant for me, for I have a feeling of being at home here at Aston Villa," he told the official club website
"I've been here for six seasons now, having started with the academy in 2006, and last season was tremendous for me and terrific for the team the way we played over the second half of a really demanding campaign.
"Like the other young players in the team, I want to keep improving as a player and keep pushing Villa as high as we can in the Premier League.
"I feel like I owe the manager and the club because the manager backed me last season after he came in and I have always felt comfortable and really supported at the club.
"The supporters, too, have been brilliant with me and they've really taken to me which I'm delighted about. It means everything to know you have support like that. The whole team feels the same way. It's great to be a part of an exciting future at Villa."
Villa boss Paul Lambert added: "Andi has shown a great work ethic and that's the big thing about him, along with his quality. He has drive and a hunger to succeed and that's vital. That's what we're looking for here at Villa.
"He got a sustained run at it last season and he showed the quality that marks him out as a natural finisher. He definitely knows where the goal is and his performances on that right side, coming off the lines, have been really great."