The 25-year-old joined Sevilla in 2007 but has not been a first-team regular in recent seasons.
He made just 19 appearances last term before being loaned out to Argentinian giants Boca Juniors.
Argentina international Perotti did show his class with four goals from eight appearances in Sevilla's successful UEFA Europa League campaign, though.
And Genoa have moved for the forward, confirming the deal in a brief statement on the club's official website.
"Genoa communicates it has reached an agreement with Sevilla for the acquisition of the sporting rights of forward Diego Perotti," it read.
"The player has signed a four-year contract."
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