Zverev posted a message on Instagram welcoming Lendl to his team with the pair having trained together in Florida this year.
The 21-year-old, known as Sascha, had been working with Juan Carlos Ferrero but split with the Spaniard earlier this year.
Lendl's manager Jerry Solomon posted two tweets, including one quoting the Czech-born tennis great.
Lendl has had two successful spells working with Andy Murray, helping the Briton secure his maiden Grand Slam title at the U.S. Open, two Wimbledon crowns and two Olympic gold medals.
The 58-year-old Lendl, who won 94 singles titles in his 16-year professional playing career, including eight Grand Slams, split with Murray for the second time in November last year.
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World number four Zverev, a towering figure at six feet six inches (1.98 metres), has won nine singles titles but has yet to get past the quarter-finals at a Grand Slam.
He heads into next week's U.S. Open having never reached the third round at Flushing Meadows.
Zverev won two titles on clay this year before warming up for the U.S. Open by winning in Washington for the second straight year.