The Portuguese will replace Luciano Spalletti who was sacked this month. Caretaker coach Sergey Semak will be in charge of the team on Wednesday for their Champions League last 16 match at Borussia Dortmund which they trail 4-2 from the first leg.
"Zenit has agreed terms on a contract with new head coach Andre Villas-Boas," the club said in a statement. "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's contract begins in March, 2014 and is valid for two seasons."
The 36-year-old, who was sacked by English Premier League club Tottenham in December, will earn 8.5 million euros (£7.1 million) per season, Russia's R-Sport reported, which would make him one of the highest paid soccer managers in the world.
"A fixed salary of 8.5 million euros has been agreed with Villas-Boas per season, while he will also be in line for bonuses for certain results," a source familiar with transfer negotiations told the state-owned news agency.
Zenit managed just one win in the Champions League group stage but finished runners-up in their section and became the first team ever to reach the knockout stages with six points.
"I think we need a breath of fresh air within the team," Zenit's Belgium defender Nicolas Lombaerts told a news conference ahead of Wednesday's game at Dortmund.
"Villas-Boas is a good coach, who has won the Europa League. We have the same experience, so hopefully together we will be able to reach new heights.
"I am sure that in terms of tactics and his man management skills Villas-Boas is a good man, therefore I am really counting on us reaching our goals."
Villas-Boas became the youngest coach to win a UEFA competition when Porto lifted the Europa League in 2011, two years after Zenit won its predecessor the UEFA Cup, to complete a treble that included the domestic league and cup.
He joined Chelsea on the back of that success when the London club paid £13.3 million to trigger his escape clause but Villas-Boas did not last the season.
Villas-Boas will bump into some familiar faces at Zenit. Brazilian forward Hulk played under him at Porto and defender Luis Neto and midfielder Danny are Portugal internationals.
He will also be aware of talented Belgium midfielder Axel Witsel, who joined Zenit from Portuguese giants Benfica.
There were other candidates for the vacant post at Zenit.
Vitesse Arnhem coach Peter Bosz, 50, was reported to be a target and the website of the Dutch newspaper De Telegraaf (www.telegraaf.nl) reported that he had held talks with Zenit in Amsterdam about potentially joining Russia's second-city club.
Former CSKA Moscow manager and veteran coach Valery Gazzaev, 59, was also linked with being handed the task of taking over at last season's Russian Premier League runners-up.
Dutch media reports said Villas-Boas was chosen by Zenit because Hulk wanted a head coach who could speak Portuguese. Hulk's agent, Jorge Mendes, is also a friend of Villas-Boas.
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