The 21-year-old Scotland international will stay on loan at Leeds until the end of the season.
“Barry is a player we have 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,” Leeds boss Simon Grayson told the club’s official website.
“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.”