Rapinoe scored six goals in the tournament, earning her the Golden Boot for the tournament’s top scorer and the Golden Ball as the top player.
The other finalist for the award was England forward Lucy Bronze.
For the men, Lionel Messi won his sixth FIFA player of the year award at the same ceremony.
Messi’s award moved the Barcelona and Argentina forward one ahead of Cristiano Ronaldo, who was also among the three finalists.
The duo has dominated the award since 2008, with their string of victories only interrupted by Luka Modric last year.
Liverpool defender Virgil van Dijk was the other finalist.
His club manager Jürgen Klopp was named coach of the year after steering Liverpool to the Champions League title in June.