Zverev fell to his knees and cheered when the match ball was hit.
World number five Zverev has found his top form at just the right time.
On the way to the Olympic gold, he beat Novak Djokovic in the semifinals and he made the process short with Chatjanov in the final.
Zverev has long been painted as not mentally strong enough to win the big titles and he lost, among other things, a 2-0 lead to a loss in five sets in the US Open final against Dominic Thiem last year.
But in the Olympic final no nerves were noticed but Zverev controlled the match.
Zverev becomes the first German tennis player to win a singles title at the Olympics since Steffi Graf won the women's singles in Seoul in 1988.