The 68-year-old replaces Sergei Tashuev whose contract ran out after he led the team to promotion last season.
Semin has also previously coached Lokomotiv Moscow, Dynamo Kiev and Mordoviya Saransk.
Anzhi went on a brief spending spree and brought high-profile names like Samuel Eto'o and Guus Hiddink into the club.
Owner Suleyman Kerimov then decided to cut costs and the team were relegated at the end of the 2013-14 season.
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(Reporting by Dmitriy Rogovitskiy, editing by Tony Jimenez)
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