Cheered on by triple Roland Garros champion and compatriot Gustavo Kuerten, Melo ended a tight contest with a splendid half volley to deny the American Bryan brothers their 17th major.
Dodig becomes the first Croatian to win a title at the French Open while Melo is only the second Brazilian to triumph on the Paris clay after Kuerten's success in 1997, 2000 and 2001.
Dodig and Melo lost the 2013 Wimbledon final against the Bryan brothers.
The top-seeded Americans got off to a solid start and claimed the first set on a tiebreak only for their third-seeded opponents to level in the same fashion.
Dodig and Melo then broke decisively in the 11th game of the decider and closed the match out to claim the trophy.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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