Villa have paid a reported £8.75 million ($11m) for Trezeguet, who also made three appearances at the 2018 World Cup and becomes the club's ninth signing of the close season.
"We're really excited to work with Trez. I've watched him a number of times," Villa head coach Dean Smith told their official website.
"He's the type of wide player that we have been looking for who is direct, causes problems for the opposition in the final third and scores goals."
Dean Smith has been very busy in the summer market, bringing in the likes of Tyrone Mings, Wesley, Matt Targett and Ezri Konza ahead of the club's first season back in the top flight.
Villa won promotion from the Championship via the playoffs last term, beating Derby 2-1 in a Wembley final back in May.
The Lions have already spent close to £100 million ($125m) in total during the current window, with a £15 million ($19m) deal for Manchester City's Douglas Luiz also expected to be sewn up in the coming days.
Trezeguet will not be eligible to play for Villa in their latest pre-season outing against Walsall on Wednesday, as he awaits a stamp on his visa.