Barcelona striker Messi’s victory in Milan was a surprise as he edged out Virgil Van Dijk, who won the UEFA player’s award last month after helping Liverpool to the Champions League last season.
Both Messi and Van Dijk are now in the running for the coveted Ballon d’Or which will be announced on December 2.
Juventus’s forward Cristiano Ronaldo had also been shortlisted for the award.
Rapinoe beat fellow World Cup winner Alex Morgan and England’s Lucy Bronze to the women’s title.
The 34-year-old won the Golden Boot for being top scorer and the Golden Ball for the best player at the World Cup, and also became the face of the tournament for her outspoken views on US president Donald Trump.