The 22-year-old winger has signed a two-year deal with the Championship club, with the option of a further season, subject to league and international clearance.
Goal reported on Sunday that Middlesbrough were closing in on a deal for Wildschut as well as Genk striker and long-term target Jelle Vossen.
Wildschut is a product of the Ajax academy but did not make an appearance for the Netherlands' most successful club before he joined FC Zwolle in 2010.
He has since played for VVV Venlo and Heerenveen, clocking up over 100 senior appearances in total, and spent the second half of last season on loan at ADO Den Haag.
Wildschut also made 10 appearances for the Dutch Under-21 side but is yet to earn a senior cap for the World Cup semi-finalists.