Kabak was unable to help Stuttgart stave off relegation from the Bundesliga last term but impressed enough to be touted as a target for several top clubs.
The Turkish defender, however, has opted for Schalke where he will link up with former Huddersfield Town boss David Wagner for 2019-20 .
Kabak started his career at Galatasaray and was named the Bundesliga's Rookie of the Season last term despite making only 15 appearances.
Schalke's sporting director Jochen Schneider indicated the club had to fight off a lot of competition to seal Kabak's signing.
"We are very happy that we have managed to win one of the biggest current European talents for Schalke," he told the club's website. "Despite very well-known competitors, Ozan Kabak deliberately chose our club.
"My thanks go especially to head coach David Wagner and Michael Reschke as technical director, who convinced Ozan decisively that the step to Schalke is the right one for him."
Sunday was a busy day for Schalke - who finished a disappointing 14th last season - with the club also confirming United States international Weston McKennie has signed a new five-year deal.
"The decision was very easy for me because I was constantly allowed to enjoy incredibly great support from the fans," said the 20-year-old, who is on international duty at the Gold Cup. "The staff were also always behind me. I'm looking forward to everything that's coming."
The 11-time USA international has enjoyed two full seasons with the Schalke first team, with both his goals for the club coming in the 2018-19 season.
He has proven himself an incredibly popular and useful player at Schalke, with his versatility providing the team with a valuable asset.
McKennie will be in action for the USA as they face Curacao for a place in the Gold Cup semi-finals on Sunday.