The Ghanaian left-back is returning to the Bundesliga having joined Chelsea from Augsburg just a year ago.
At the time it was reported that Chelsea were to pay £14m up front plus bonus payments of up to £6m due should he play more than 100 matches.
Rahman, 22, had signed a five-year deal at the club and provided cover for the first-choice left-back César Azpilicueta last season but does not appear to figure in the new manager Antonio Conte’s plans.
Rahman made 23 appearances last season, 19 of them starts, with his debut also his first career game in the Champions League, a 4-0 win over Maccabi Tel Aviv.
Schalke finished fifth in the German top flight last season and have a former Chelsea striker Franco Di Santo in their squad. Baba will be reunited with his former Augsburg manager Markus Weinzierl who took charge of Schalke earlier this summer.
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