Itoje, 22, helped England complete the Six Nations Grand Slam and was part of the squad that secured a 3-0 series whitewash of Australia down under.
England captain Hunter, 31, was ever-present throughout 2016.
New Zealand fly-half Beauden Barrett won the men's player of the year award.
Barrett, 25, is the fifth successive player from the world champion All Blacks to receive the award, after Dan Carter (2012 and 2015), Kieran Read (2013) and Brodie Retallick (2014).
Itoje, his Saracens and England team-mates Owen Farrell and Billy Vunipola, New Zealand's Dane Coles and Ireland's Jamie Heaslip were also shortlisted.
Itoje is currently injured and missed England's 37-21 win over South Africa on Saturday.
Steve Hansen was named coach of the year, and his All Blacks were team of the year having set a new record for winning 18 successive Tests.
South Africa's Seabelo Senatla and Australia's Charlotte Caslick were respectively the men's and women's sevens players of the year.
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England forward Maro Itoje was named breakthrough player of year and compatriot Sarah Hunter won women's player of the year at the World Rugby awards.