Woolright is the former drummer of Auckland nu-metal band Blindspott, who had a string of local hits throughout the noughties. He is now a member of I Am Giant.
Bassingthwaighte is a former cast member of Neighbours who went on to become the singer in electro-pop band Rogue Traders before embarking on a solo career. She has been a judge on The X Factor Australia.
Woolright told hosts on The Edge Radio station he had got a phone call about the producers yesterday and at first thought it was a prank.
He said he was excited and "absolutely freaking out" about the role.
Bassingthwaighte's debut solo album 1000 Stars topped the Australian charts when it was released in 2009.
Bassingthwaighte is looking after the boys in the competition while Woolright will be in charge of the bands.
"I think we are going to win this hands down," said Bassingthwaighte, who has been an X Factor Australia judge for four seasons, though she hasn't won any of the competitions.
The two new judges replace Willy Moon and Natalia Kills, who were axed on Monday following a bullying controversy surrounding contestant Joe Irvine on Sunday night's show.
Neither new judge offered any strong opinions on the controversy which has got them their roles with Bassingthwaighte saying: "Look, I think the whole point of the show is about nurturing talent."
The news was announced at 4pm on a local radio station.
