The 23-year-old, who has represented England at under-20 and under-21 level, had joined Villa on loan in January and made 12 appearances in the second-tier Championship.
"Aston Villa have taken up the option to permanently transfer Kortney Hause from Wolverhampton Wanderers," Villa said in a statement.
Dean Smith's side have already signed Spanish winger Jota and Dutchman Anwar El Ghazi after their Championship playoff final win over Derby County last month.
They have also agreed a deal to bring in Brazilian striker Wesley from Club Brugge.
Villa, back in the top flight after a three-season absence, kick off their Premier league campaign against Tottenham Hotspur on Aug. 10.
