Kramer, 50, was sacked by Arminia Bielefeld in April as the club made an unsuccessful last-ditch bid to avoid relegation from the German top flight.
He has previously had spells in charge of Greuther Fuerth, Fortuna Duesseldorf and several of Germany’s national youth teams.
“As a promoted side, even as Schalke 04, so not your classic promoted side, the only goal can be to avoid relegation. The Bundesliga will be a huge challenge for us,” Kramer said in a statement.
On his coaching staff, Kramer will have two club legends in Mike Bueskens, part of the Schalke team which won the 1997 UEFA Cup, and ex-Germany striker Gerald Asamoah.
Schalke finished bottom of Germany’s top tier in 2020/21 but came straight back up after winning the second division title.
“With 160,000 members and many millions of fans, Schalke 04 is one of the biggest clubs in Germany,” added Kramer.
“I’m looking forward to standing on the sideline as head coach and playing my part in achieving our collective goals.”