The band's former guitarist and drummer responded to speculation that the group would get back together with frontman Morrissey and bassist Andy Rourke for live shows this autumn.
Marr wrote on his official Facebook page: "The rumour of the Smiths reunion is untrue. It's not happening."
Speaking to Beat Wolf Radio, Joyce said: "It's not happening folks, as far as I know. Which could be a good thing.
"Now if it was going to happen sans me then, yeah, I don't know. Avec me, then I would have known about it, wouldn't I?"
Of the possibility that the band ever reforming at some point in the future, he added: "Who knows, in the future... only time will tell."
He later added in a press statement: "After today's reports of The Smiths reforming I can confirm that they are NOT."
> Poll - Should The Smiths ever reform?
Watch The Smiths perform 'William, It Was Really Nothing' live on Top of the Pops in 1984 below: