The award, at a gala prizegiving ceremony in Paris on Friday night, followed a vote by media permanently accredited to the governing International Automobile Federation's world championships.
Kubica saw off rivals on a shortlist of 10 that included Red Bull's quadruple Formula One world champion Sebastian Vettel, world rally champion Sebastien Ogier and Red Bull principal Christian Horner.
Ogier and Volkswagen co-driver Julien Ingrassia won the FIA's new 'Moment of the Year' award, chosen by followers of the FIA's facebook page from a shortlist of 12 videos that did not feature any Formula One races.
Vettel was officially presented with the Formula One champion's trophy for the fourth successive year.
The season-ending Brazilian Grand Prix won the award for the best promoter while Britain's Sky Sports television won the broadcasters' trophy for the second year in a row.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
