The length of the contract with the 19-year-old, who represents Serbia at Under-21 level, was not given.
Jovanovic made his debut for Red Star in August 2014 and scored two goals in 32 games in the Serbian championship.
Zenit are sixth in the Russian Premier League. They lost the first leg of their Champions League round-of-16 match with Benfica 1-0 and host the return leg in St. Petersburg on March 9.
(Reporting By Dmitriy Rogovitskiy; editing by Clare Fallon)
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