The shock news, confirmed by Variety, comes after the departure of the band's longtime guitarist Lindsey Buckingham.
Variety reported Mike Campbell, a guitarist in Tom Petty & The Heartbreakers, and Finn would join the group on their upcoming tour.
"Fleetwood Mac has always been about an amazing collection of songs that are performed with a unique blend of talents," Mick Fleetwood said.
"We jammed with Mike and Neil and the chemistry really worked and let the band realize that this is the right combination to go forward with in Fleetwood Mac style.
"We know we have something new, yet it's got the unmistakable Mac sound."
The group said it was "thrilled to welcome the musical talents of the caliber of Mike Campbell and Neil Finn into the Mac family".
With tour dates to be announced shortly, they'll be "performing all the hits that the fans love, plus we'll be surprising our audiences with some tracks from our historic catalogue of songs.
"Fleetwood Mac has always been a creative evolution. We look forward to honoring that spirit on this upcoming tour."
Known for hits like Dreams and Go Your Own Way, Fleetwood Mac formed in 1967 and still tour regularly. Fronted by Stevie Nicks, they were last here in 2015.
Neil Finn has just released his latest solo album Out of Silence.
