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.
