The 23-year-old striker has signed a four-year contract after the clubs agreed an undisclosed fee, which local newspaper the Derby Evening Telegraph believes to be in the region of £2million.
Weimann struggled to establish himself in Villa’s first team under new boss Tim Sherwood but made 20 league starts overall last season.
And he has told Derby he is looking forward to a new challenge as they attempt to reach the Premier League under their new head coach Paul Clement.
The Austria international said: “I’m excited to be here and I’m looking forward to the new challenge.
“Derby have plans to be successful and get promoted and that’s what attracted me here; I want to be part of that.
“The opportunity to play first-team football and drive the team to promotion is something that I want to do.
“I know how difficult the Championship is – I’ve played in the league on loan at Watford a few years ago – and it was a tough league back then.
“With the set-up here and the players we have – and those that we are looking to sign – I feel that we have a good chance to get promoted.”
“I’ve had chats with the head coach and people around the club and it seems it’s an exciting time for Derby County.”