His decision comes after last Saturday's show, where viewers saw Osborne throw glasses of water over Walsh.
The spat arose from the previous episode of 'X Factor', where Walsh decided to give Irish girl band The Conway Sisters the chance to stay in the show, and dump the London singer Maria, who is being mentored by Sharon Osborne.
Osborne took the decision badly, accusing Walsh of choosing The Conway Sisters because of the "Irish mafia". The feud bubbled along in to last weekend's contest, but Osborne had her revenge when she chose to boot Walsh's act, Nicholas. Walsh is now left with only one contestant on the show -- Shayne, the bookies' favourite to win.
The ignominy for Walsh was worsened when Cowell made comments in The Sun and on ITV1's 'This Morning', saying that Walsh was "bland" and "an idiot".
Walsh is quoted in The Sun as saying: "I've been totally humiliated and undermined by both of them. This has caused me nothing but stress.
"The final straw was Sharon with the water and being booed by the audience and then Simon Cowell saying I was an idiot and stupid. I've had enough. I'm going back to Dublin. I'm not going to put up with it any more."
The paper goes on to report that Cowell, whose production company Syco is behind 'X Factor', has pleaded with Walsh to return to the show.
"If I've offended him I apologise. We want him back," Cowell said.
Producers are in discussions with Walsh to try to get him to return to the series. He has signed up to judge a further series of 'X Factor', along with Osborne.
This season of 'X Factor' has been marked by a high degree of bitchiness between all three judges, who frequently accuse each other of choosing bad songs and mismanaging their acts, and of being unimaginative.
Six contestants remain in the programme: former binman Andy, dancer Chico and disco diva Brenda, all mentored by Osborne; The Conway Sisters and Journey South, for Cowell; and Mancunian Shayne, for Walsh.
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