The 17-year-old midfielder, who only made six Allsvenskan appearances for the Swedish club, was invited for a trial with Schalke in November.
Sivodedov has done enough to earn himself a three-and-a-half year deal with Roberto Di Matteo's side that runs until June 2018.
"It is great for me but at the same time I have mixed feelings," Sivodedov told the official Djurgardens website.
"I have played for Djurgardens all my life and it is the club in my heart. But this is a unique chance for me and I have based my choice on facts together with my family and Djurgardens."
"I think the best football in the world is played in Germany. Schalke is a great club with unique capabilities that give me every chance to develop into a better."
It marks another foray into the transfer market for Schalke this month after they completed the loan signing of defender Matija Nastasic from Manchester City.
Schalke, who are fifth, resume their Bundesliga campaign at home to Hannover on January 31 after the mid-season break.
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