"It is an amazing feeling when you get to win a tournament, especially in Dubai in front of so many fans," Fiji captain Osea Kolinisau told the tournament website.
"There’s a feeling of relief in the team. The game of sevens is getting harder. There are no easy games ahead and we are grateful to have won here."
Fiji earlier overcame New Zealand 19-5 in the semi-finals and England beat the United States 24-19.
The Americans, who upset the All Blacks in the group stage, repeated the feat by defeating the New Zealanders 31-12 in the third-place playoff.
There are 10 rounds in the World Rugby Sevens series before the sport makes it first appearance at the Olympics, in Rio de Janeiro next year.
(Reporting by Ed Osmond, editing by Alan Baldwin)
