The 18-year-old penned a two-and-a-half-year contract after agreeing personal terms and passing a medical earlier on Friday with the deal also involving add-ons and a sell-on clause.
Hause joined Wycombe from Birmingham in 2012 and made 31 appearances for the League Two club, scoring twice.
Head of Football Development and Recruitment Kevin Thelwell told the club's official website: "Kortney is a left-sided centre-half who, for an 18-year-old, has played an impressive number of games at a high standard.
"One of the remits of Stuart Webber and our recruitment team is not only to identify players who can go straight into the first team but also players who have the potential to go into the first team moving forwards in the future.
"That is what we have done in signing Kortney, and we are delighted he has agreed to join the club."