The Portugal international, who had a starring role for his national team at EURO 2012, joins the Ukrainian side after two seasons with the Grifoni.
A statement from Genoa read: "The deal that has seen Miguel Veloso join Dynamo Kiev has been successfully completed for all parties concerned."
The 26-year-old Veloso made 29 league appearances for Genoa last season and has signed a four-year contract with Dynamo.
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