The Belgium international had vowed to stay at Zenit for another season and coach Mircea Lucescu confirmed that he had rejected a move to Everton.
However, the 27-year-old will leave Belgium's training camp to undergo a medical at the Serie A champions on Wednesday.
Massimiliano Allegri's side will pay around €18 million for the midfielder with more to come through bonuses.
Witsel joined Zenit in 2012 and has won a Russian Premier League title as well as a Russian Cup and Super Cup. He is contracted to the club until June 2017.
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