Argentina and Barcelona forward Lionel Messi (L) is presented with the men's player of year award by FIFA president Gianni Infantino. (AFP)

Lionel Messi won the FIFA Men’s Player of the Year award on Monday with Megan Rapinoe bagging the women’s prize to cap a historic year for the United States’ World Cup icon.

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.

Juventus’s forward Cristiano Ronaldo had also been shortlisted for the award, but did not attend the ceremony as he lost out to his rival in the famous La Scala opera house.

Both Messi, 32, and Van Dijk, 28, are now in the running for the coveted Ballon d’Or which will be announced on 2 December.

Rapinoe beat fellow World Cup winner Alex Morgan and England’s Lucy Bronze to the women’s title, with US coach Jill Ellis winning women’s coaching award.

Megan Rapinoe (R) and US teammate Alex Morgan (L) arrive for The Best FIFA Football Awards ceremony in Milan. (AFP)

The 34-year-old Rapinoe 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.

Messi was top scorer in the Champions League last season with 12 goals before Barcelona was dumped out by Liverpool in the semifinals, Barca throwing away a three-goal first-leg lead with a humiliating 4-0 defeat at Anfield.

The Argentine also won the European Golden Shoe after scoring 36 goals, won La Liga title with Barcelona and helped Argentina to bronze at 2019 Copa America.

Van Dijk had been bidding to become just the second defender — after Italian Fabio Cannavaro in 2006 — to be recognised by FIFA as the world’s best player.

And he missed out on completing a treble for Liverpool with manager Jurgen Klopp winning the men’s coach of the year award and Alisson Becker the goalkeeper prize.

Klopp won the Champions League with Liverpool ahead of two other Premier League coaches — Tottenham’s Mauricio Pochettino, who reached the European final, and Manchester City’s Pep Guardiola.

“It is great, nobody expected this 20, 10, five, four years ago that I would be standing here,” said the 52-year-old German who joined Liverpool in 2015.

“I have to say thank you to my outstanding club Liverpool FC. Those who don’t love it don’t have a heart.

“As a coach you can only be as good as your team. I’m really proud of being coach of such an incredible bunch of players.”

Two-time women’s World Cup-winning coach Ellis, beat Dutch coach Sarina Wiegman, runner-up in France 2019, and England’s Phil Neville for the award.

“The World Cup really was a showcase, the world fell even more in love with the game,” said 53-year-old Ellis, who will step down from the team in October.

Romanian-born Hungarian forward Daniel Zsori won the Fifa Puskas Award for the best goal, beating strikes from Messi and Juan Fernando Quintero.

The 18-year-old forward, on his debut, scored a spectacular overhead kick to win the game for his side Debrecen against Ferencvaros in stoppage time.