Abil beat six other candidates who had been nominated, securing 41 votes.
It was the third attempt by the college to elect a new head of state in two days, after two earlier elections saw no one candidate attaining the required two-thirds of the vote.
Abil comes from Tanna and is a former cabinet minister in the first Vanuatu government after the country gained independence in 1980.
He succeeds Kalkot Mataskelekele whose term as president ended last month.
Mataskelele’s nomination for re-election was earlier supported by several MPs including some within government before the ruling coalition finally agreed to support Abil with their votes.
