The 23-year-old is poised to join imminently following Villa’s decision to trigger a clause included in the agreement which saw him join from Molineux on loan in January.
Hause made 12 appearances during a successful stint at Villa Park, helping Dean Smith’s team clinch a return to the Premier League through the play-offs.
The former England under-21 international was a major factor in the transformation of Villa’s defence from one of the weakest in the Championship to one of the strongest.
He is viewed by boss Smith and his coaching as a player who still has plenty of room left to grow.
Hause will follow Jota through the door after the winger on Thursday became the Villa’s first signing since promotion by completing an anticipated switch from Blues.
The 27-year-old has agreed a two-year deal and has become the first player to join Villa directly from their rivals since Alan Curbishley in 1983.
It is believed Villa have paid around £4million for Jota, with midfielder Gary Gardner moving in the other direction to St Andrew’s as part of the deal.