Bowery becomes the sixth new signing at Villa this summer following defenders Ron Vlaar, Joe Bennett and Matt Lowton, and midfield duo Brett Holman and Karim El Ahmadi.
His father Bert Bowery was also a striker who played for Nottingham Forest under Brian Clough before moving to the North American Soccer League in 1976.
Villa boss Paul Lambert said: "Jordan is a good player. The hunger will be there for him and he could surprise a few people.
"He's a good lad, he's strong and powerful. He's played over 100 games in the Football League and cup football, so he's battle-hardened.
"He's one for the future but if he steps up to the plate like I think he can then I would have no hesitation in throwing him in, none whatsoever."
Bowery played 40 games for Chesterfield in League One last season and also made eight appearances in Cups, scoring 12 goals in all competitions.
He said: "This is a Premier League club with so much history, a massive club, and I'm really excited.
"Paul Lambert talked about wanting to bring in young, raw, hungry talent, players who want to improve here and want to get to this level and stay at this level.
"I think that's what he's looked at in me."