The former Bournemouth manager leaves Wolves second from bottom in the Premier League table, four points from safety.
It is also understood Wolves had sounded out Graham Potter and David Moyes to replace O'Neil, but both turned down the club's advances.
Wolves have also approached Carlos Corberan, who is in charge of West Bromwich Albion.
A move for Corberan would be a bold move by Wolves' powerbrokers given West Brom are the club's arch rivals.
O'Neil's axing comes less than 24 hours after he suffered a demoralising 2-1 defeat to Ipswich Town at Molineux.
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The Tractor Boys took the lead through an own goal from Matt Doherty but equalised in the 72nd minute via Matheus Cunha.
However, Ipswich nicked all three points thanks to Jack Taylor's second-half stoppage-time strike.
Chaos ensued after the full-time whistle as Wolves defender Rayan Ait-Nouri had to be carried off the pitch by teammate Craig Dawson.
Ait-Nouri was given a second yellow card after the contest, meaning he is suspended for Wolves' trip to Leicester City next Sunday.
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Goalscorer Cunha was also visibly irate and needed to be ushered down the tunnel to avoid further punishment.
Footage on social media of Cunha ripping the glasses off the face of an Ipswich Town staff member quickly circulated on social media.
The Ipswich loss marked the fourth-straight defeat for O'Neil's side and the second consecutive game marred by ugly post-match scenes.
After Wolves' 2-1 loss to West Ham United last Monday, Mario Lemina was involved in a tussle with Hammers captain Jarrod Bowen in which both players went tumbling to the ground.
O'Neil and his coaching staff were quickly on the field as they looked to diffuse the situation, but it only got worse.
Lemina soon squared up to assistant coach Shaun Derry as the two pressed their foreheads together before Wolves teammate Toti Gomes pulled the midfielder away.
As a result of his involvement in the post-match fracas, Lemina was stripped of the captaincy.
O'Neil's departure means Wolves are now looking for a fourth permanent manager since Nuno Espirito Santo left at the end of the 2020/21 season.
Bruno Lage succeeded Nuno but lasted only 51 games before he was given his marching orders in October 2022.
Former Spain and Real Madrid boss Julen Lopetegui arrived at Molineux as Lage's replacement.
However, he left on the eve of the 23/24 season after he learned of the club's financial constraints.
Whichever manager is appointed as O'Neil's successor will have plenty of work on their hands if they are to keep the club afloat in the Premier League.
The club has shipped a league-most 40 goals from just 16 games, which equates to an average of 2.5 goals per game.
Leicester City have conceded the second-most with 34 goals.
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Should Wolves maintain the alarming figure, they would be on track to have conceded the second-most goals in a 38-game Premier League season.
Sheffield United hold the record with 104 goals conceded in the 23/24 campaign, with Derby County in second thanks to their tally of 89 goals conceded in their infamous 07/08 term in which they finished with the fewest points in Premier League history.