"He doesn't like me and I don't like him, that's it," Liam said.
The brothers have always had a fractious relationship, and a string of tours have fallen apart over the past 15 years.
But until now, neither Gallagher has officially quit the group.
Alan McGee, who discovered Oasis in 1993 and signed them to his Creation Records label, said the rift was "more serious than anything that's ever happened".
"It's obviously the worst fall-out that they've ever had, and they've had some pretty bad ones," he told BBC News. "This is a pretty serious one. But they love each other, they'll come back together."
Noel and Liam would go on to make solo albums, he predicted, before getting back together.
"I think you'll have a reunion tour in about five years time. They love each other. When people love each other, they'll always make peace."
The band were at their peak in the Britpop years of the mid-1990s
NME writer Hamish McBain said: "The relationship between Noel and Liam has been frosty over the last tour, to say the least, but it's been frosty before.
"Noel has left tours before, Liam's not showed up for gigs before, and they've carried on. But this, certainly the way Noel's presented it on the Oasis website, it does feel like it has a degree of finality to it."
BBC 6 Music DJ Steve Lamacq said the scale of the world tour appeared to be the last straw.
"With the Gallagher brothers, I think you never say never, do you? But it's after a very, very long tour this and I think it was quite ambitious," he told BBC Radio 5 live.
"Maybe this was asking a bit too much, with this fractious relationship as it is at the moment."
Oasis fans used Twitter to respond to the news that lead guitarist Noel had quit.
PsychedelicAdam posted: "Noel Gallagher leaves Oasis? Gutted, no more Oasis then I guess, they were one of my favourite bands."
The BBC's Jane Witherspoon spoke to Noel Gallagher in July
Wolvolass said: "I feel sick, sooo many good memories and gigs seeing Oasis over the years."
MattGriffin added: "This is the worst day ever."
Oasis formed in Manchester in 1991, with the brothers joined by Paul Arthurs, aka Bonehead, on guitar, Paul McGuigan, aka Guigsy, on bass, and Tony McCarroll on drums.
They had eight UK number one singles and amassed 15 NME Awards, five BRIT Awards, nine Q Awards and four MTV Europe Music Awards.
In February 2007, Oasis received the BRIT Award for outstanding contribution to music.
The Gallagher brothers have featured regularly in tabloid newspapers for their sibling disputes, wild lifestyles and public feud with rival Britpop band Blur.
The final line-up consisted of guitarist Gem Archer and bassist Andy Bell, as well as unofficial drummer Chris Sharrock.
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