The 21-year-old Scotland international will go straight into Simon Grayson's squad for Tuesday night's league clash at Preston.
Grayson said: "Barry's a player we've been tracking for a while. Circumstances have now changed where Villa are in a position to let him join us and I'd like to thank them for agreeing to the move.
"He's had the opportunity to go to nearly every other team in the Championship so for him to come here makes it all the more pleasing.
"He's used to this division and he played a major part in Blackpool's run to get promoted last season, so he has experience and he fits the bill perfectly for us."
Bannan played alongside Leeds winger Robert Snodgrass for Scotland against Northern Ireland last month.
Source: PA
Source: PA