Kanchelskis, whose searing pace made him an important part of the Manchester United side that clinched two Premier League titles in his four-year spell at the club from 1991, also played for Everton, Fiorentina, Glasgow Rangers and Manchester City.
The former Russia international ended his playing career in 2006 and has since taken on head coach roles at Russian clubs Torpedo-ZIL Moscow and FC Ufa and Latvian side Jurmala.
The 46-year-old replaces Sergei Shustikov, who died on Jan. 7 from a heart attack at the age of 45.
Solyaris play in the Second Division West, which is the third tier of Russian football. They are second in the table, six points behind the leaders.
(Reporting By Dmitriy Rogovitskiy; editing by Toby Davis)
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