The 22-year-old has signed a five-year deal with the Black Cats and will join the club for an undisclosed fee.
“Simon is an excellent young goalkeeper and he has a lot more to offer. I’m sure he will push our current goalkeepers all the way next season,” Sunderland boss Steve Bruce told the club’s official website.
“He is a player that we have watched on a number of occasions, as have a lot of clubs in Europe over the last couple of seasons. We’re delighted to bring him to Sunderland.
“He’ll come back ready for the start of pre-season training and will be looking to push for a place in the team.”