Villa are splashing out an initial £18million for Bent but additional add-ons mean the final figure could rise by another £6million.
The England player is in line to make his debut in Saturday evening's home Barclays Premier League clash with Manchester City.
The four-and-a-half-year deal was completed on Tuesday after Bent agreed personal terms and passed a medical.
Bent, 26, said: "Aston Villa is a massive football club and as soon as I knew they were interested in signing me I wanted to join. The size of the football club and the history of the club are major reasons for me coming here.
"There are some top, top players here too, real quality, and I've been able to speak to the manager and the owner about their ambitions for the club. I'm very excited about being a part of what we hope to achieve."