The 25-year-old has 18 months left to run on his contract with Leverkusen, but agreed terms with the Gelsenkirchen club, who have met the terms of a clause in his contract.
He has put pen to paper on a four-year deal for the Royal Blues.
"Sidney Sam has not only proven with his strong performances this season what kind of an impact he can have in attack," said Schalke's director of sport Horst Heldt.
"He can play in a variety of positions, is very ambitious and would like to achieve a lot with Schalke.
"We're really delighted that he has chosen to join the Royal Blues."
Sam is a candidate to play at the World Cup this summer, if he can prove his form after a lengthy injury absence.
The former Kaiserslautern forward has not featured since November 23, when he pulled muscle fibres, although he is now close to a return to training and could be back for the second half of the season.
His partnership with Stefan Kiessling and Heung-Min Son in the Leverkusen attack has contributed to the Westphalian club occupying second spot in the Bundesliga over the winter break.
Capped five times by Germany, Sam has scored seven goals in 13 games this season for Leverkusen.