Mr Kabua, a veteran politician and former cabinet minister who is the second son of founding president Amata Kabua, won the vote by 20-12 with one abstention.
Mr Kabua has previously held the health and internal affairs ministerial portfolios.
Mr Kabua was seen as a presidential candidate who could bring rival candidates together as a leader acceptable to most factions, said RNZ Pacific correspondent Giff Johnson.
He described Mr Kabua as a likeable man, with a "low-key personality".