The four-times champions have failed to win any of their opening three league games this season and are 12th in the table with one point.
Velev guided Levski Sofia to the title in 2009 but was then sacked by three teams in just over two years. He was fired by Slavia Sofia in 2011 and Lokomotiv Plovdiv last October.
Genov, who previously coached Cherno More and Lokomotiv Plovdiv in the Bulgarian top flight, has signed a two-year contract.
His first game will be at home to Chernomorets Burgas next Monday.
(Reporting by Angel Krasimirov; editing by Tony Jimenez)
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