The 17-year-old centre back has played eight times for the first-team since making his debut for Gareth Ainsworth's side back in November.
Hause becomes he third Wycombe youngster to sign a new deal in recent weeks after Matt Ingram and Matt McClure put pen to paper.
Blues boss Gareth Ainsworth told the club's official website: "It's a hugely important signing for the club. I've said I want to protect the assets of the football club.
"What he's done already as a 17-year-old proves how far he can go in the game.
"I believe he may play at the highest level and to sign somebody like that and have them associated with Wycombe is great for the club and its future. I'm really pleased we've been able to keep hold of him for another couple of years."
- Sports & Recreation
- Gareth Ainsworth