Fleetwood also opened up about the firing of former bandmate Lindsey Buckingham, saying "we all wish him well".
"In truthful language, we just weren't happy," he said. "And I'll leave it at that in terms of the dynamic.
"If you know anything about the history of this band, it's sort of peppered with this type of dramatic stuff," he said, referencing the band's many changes over the years.
Fleetwood Mac announced in April that Neil Finn would be joining the band along with Campbell.
"Two weeks ago I received a wonderful invitation to be a part of a truly great band. A few days later I was standing in a room playing music with Fleetwood Mac," Finn said in a statement.
"It felt fresh and exciting, so many great songs, a spectacular rhythm section and two of the greatest voices ever.
"Best of all, we sounded good together. It was a natural fit. I can't wait to play some more."