The Portuguese tactician, who had been out of work since being sacked by Spurs following their humiliating defeat by Liverpool in December, has been handed a two-year contract.
Zenit confirmed Villas-Boas will be officially presented to the media on March 20.
A short statement on Zenit's website read: "Zenit has agreed terms on a contract with new head coach André Villas-Boas.
"The contract will be signed and Mr. Villas-Boas will be presented in St. Petersburg as Zenit's new head coach on March 20. Mr. Villas-Boas' contract begins in March, 2014, and is valid for two seasons."
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