Manager Sam Allardyce lined up the former Wigan and Sunderland defender when Villa first approached Rovers about Warnock but wanted the transfers to occur simultaneously.
"We've got the deal done. We've got an experienced player who is desperate to play football again, having missed it at Spurs," said Allardyce.
"The experience of the player, the adaptability of the player in a number of positions and his past record means we will have a good player on our hands and will not miss Warnock too much.
"We all know his favourite position is right-back. We are well covered there, but he can play centre-back and left-back."
The Frenchman is unlikely to play in his preferred position because Allardyce has already signed Lars Jacobsen and Michel Salgado this summer.
Chris Samba and Gael Givet are the only two fit centre-backs, captain Ryan Nelsen currently sidelined with a knee injury - while 21-year-old Martin Olsson is the only recognised left-back, although Givet has also played there.
However, the Rovers boss is confident Chimbonda's experience and desire to play regularly will allow him to adapt quickly.
"He was eager to get away from Tottenham, because he has not played enough games for them and he just wants to play football," said Allardyce.
"When you meet someone who tells you they just want to play football it is a good thing from the start.
"When you see what he has achieved in his Wigan and Tottenham early days we want him to come and emulate that at Blackburn, whichever position we pick him in.
"We had to scurry around for the last few days and we think we have found a very successful and experienced player to come and fill the gap Stephen has left."
Despite Allardyce continuing to be linked with other players, he insists this is his last transfer before the window closes on Tuesday after reluctantly letting Warnock go.
"It is like most things today. You don't want them to leave, but once it is all done and dusted there is very little you can do about it," he said.
"When the player does not want to stay you try to maximise for the club the best possible deal and then move on.
"It is disappointing and is not something I expected. But that is the way it is in this bizarre transfer window."