Gribbin, who has a solo career under the name Joe Echo, met INXS guitarist Andrew Farriss at a party and the pair started writing and playing together.
Gribbin is the replacement for J.D. Fortune, an American singer who joined the band after winning the Rock Star: INXS competition but was fired for a second time last year. The band's original frontman, Michael Hutchence, committed suicide in 1997.
The first song featuring Gribbin on vocals, a demo called Tiny Summer, has just been released on the band's website and has had positive reviews.
The identity of the vocalist had been kept secret, leading to many speculative press reports that it was U2's Bono at the front.
Ironically, Gribbin recently wrote eight of the songs for the feature film Killing Bono, about the famous Irish band, that was released in Europe this year.
Gribbin, from Belfast, was also nominated for a Grammy last year as co-writer of Madonna's hit Celebration.
He is the latest of many singers to take the place of frontman Michael Hutchence, who died in 1997. They have included Jimmy Barnes, Jon Stevens and Terence Trent D'Arby.
Farriss tells Billboard that he and the rest of INXS do not "have a master plan" regarding how they will move forward with Gribbin, but that they are "just really enjoying being creative" and "experimenting with a whole range of things" in the studio.
"A baptism of fire is the best way to describe the live shows, I think," Gribbin tells Billboard. "In a way I'm slightly nervous, and in another way I'm unbelievably excited. It's a wonderful, proud moment for me. It's a real feeling of achievement to have a band of INXS' stature believe in me as a performer and a singer. It's genuine dream-come-true, fairy-tale stuff for me. I'm still waking up in the morning here in Australia going, 'How did I get here?'"
Before then, the new line-up will make its debut in Peru before playing their first Australian show as part of the world sailing championships in Perth on December 3.