Carter, 33, helped the All Blacks to a 34-17 win over Australia in Saturday's World Cup final at Twickenham.
He has announced his international retirement after scoring a record 1,598 points in 112 appearances.
The All Blacks won the team of the year and Australia's Michael Cheika was named coach of the year.
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Carter, who also won in 2005 and 2012, joins team-mate and All Blacks captain Richie McCaw as the only triple winners of the award, which was first given in 2001.
The five other nominees for the award were All Blacks team-mate Julian Savea, Australia flanker Michael Hooper and number eight David Pocock, Wales lock Alun Wyn Jones and Scotland scrum-half Greig Laidlaw.
Carter is joining French club Racing Metro, where he will become the sport's highest-paid player.
The World Rugby Awards winners were selected by an independent panel of judges, chaired by Australia's 1999 World Cup-winning captain John Eales and made up of former internationals, media and the teams who took part in the World Cup.
New Zealand fly-half Dan Carter was named World Rugby player of the year for a third time at a ceremony in London on Sunday.