The Ghana international, 22, made 51 appearances for Bundesliga side Augsburg before moving to Stamford Bridge on a five-year deal last August.
Raman made his Chelsea debut in the Champions League and went on to make 23 appearances for the Blues.
His return to Germany reunites him with former Augsburg manager Markus Weinzierl, who took over as Schalke manager in June.
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Schalke have signed Chelsea defender Baba Rahman on a season-long loan.