The 24-year-old, a former Germany under-21 international, joins the Belgian side after three seasons in Tilburg.
A young but experienced goalkeeper, Wellenreuther has become the undisputed number one for Willem II in recent years.
His good performances this season helped Willem II finish a respectable fifth in the Eredivisie and achieve Europa League qualification.
Wellenreuther has signed a contract with Anderlecht until 2024.
Bienvenue au Sporting @Timonwellle 🟣 ⚪ Jong én ervaren. Lef én uitstraling. Tweevoetig. Jeune et expérimenté. Mentalité. Et la volonté de progresser. https://t.co/HJWZPclhDI https://t.co/DoxpJOM2sT pic.twitter.com/NZPfXpkvrp
— RSC Anderlecht (@rscanderlecht) June 5, 2020