Dutchman Stevens succeeds Ralf Rangnick, who resigned last week due to exhaustion syndrome.
It is the 57-year-old's second spell in charge of the Gelsenkirchen club, having also led them from 1996 to 2002 - during which time the club won the 1997 UEFA Cup and the DFB-Pokal in 2001 and 2002.
In 1999, a poll of Schalke fans saw him voted the club's coach of the century.
After leaving the club in 2002, Stevens joined Hertha Berlin before spells with Cologne, Roda JC, with whom he started his coaching career, Hamburg, PSV Eindhoven and Salzburg.
Stevens was also in the running for the current vacancy at Hamburg following the sacking of Michael Oenning before they pulled out after learning of his willingness to discuss a deal with Schalke.
The Royal Blues are fifth in the Bundesliga and take on Maccabi Haifa in the group stage of the Europa League on Thursday night.