The 28-year-old was charged by the Football Association on Thursday for punching Rovers' Norway midfielder Morten Gamst Pedersen in the chest, which was not seen by the referee.
"I fully accept that I was in the wrong on this occasion and accept the charge that the FA have brought against me," Barton said in a club statement before apologising to all involved.
"This season I have really been enjoying my football and although I have been on the receiving end of a few robust challenges I have, up until now, remained calm in the face of provocation and just carried on with the game.
"But I hold my hands up, I reacted badly to the situation on Wednesday night and I deeply regret it."
Barton was given until Friday to reply to the charge and under the FA's fast-track regulations his admission means he will now be handed a standard three-match ban.
The incident is the latest in a long list of disciplinary problems faced by the former Manchester City player, who joined Newcastle in June 2007. He was jailed in 2008 for assault.
Newcastle manager Chris Hughton said: "He has worked so hard on his game this season, but he knows that he can't react the way he did on Wednesday."
THE LIFE AND TIMES OF JOEY BARTON
April 2004 - Storms out of Eastlands before kick-off after being axed from the Manchester City side to face Southampton.
July 2004 - Sparks a mass brawl in a pre-season 'friendly' against Doncaster.
December 2004 - A Christmas bash for Manchester City players sees him stub a lit cigar into the eye of young team-mate Jamie Tandy. He is fined six weeks' wages by City.
May 2005 - Breaks the leg of a 35-year-old pedestrian while driving his car at 2am in Liverpool city centre.
June 2005 - Involved in a spat with a 15-year-old Everton fan at City's team hotel in Bangkok. Again he is fined by City.
October 2006 - The bad blood with Everton fans continues in 2006 when he drops his shorts in the direction of home fans at Goodison Park. He is fined and warned by the FA for his conduct.
December 2006 - Blasts England players releasing autobiographies after an unsuccessful World Cup campaign. "England did nothing in the World Cup, so why are they bringing books out? 'We got beat in the quarter-finals, I played like s***, here's my book'. Who wants to read that? I don't," he says.
February 2007 - Makes his England debut against Spain, replacing Frank Lampard, one of the players he was thought to have aimed his earlier criticism at.
March 2007 - Arrested on suspicion of assault and criminal damage in an incident involving a taxi driver. He is alleged to have ripped out the cabbie's radio because he would not wait at a McDonald's drive-through while Barton got food. He is later found not guilty of vandalising the taxi. His cousin, Joshua Wilson, 19, admitted doing the damage.
May 2007 - Involved in a training ground incident with Manchester City team-mate Ousmane Dabo, who presses charges. Barton admits assault and in July 2008 is given a four-month suspended jail sentence. In November 2008 he is also given a six-match ban, with a further six suspended, after admitting an FA violent conduct charge relating to the incident.
June 2007 - Sold by City to Newcastle Utd for £5.8 million. Aims parting shot at City boss Stuart Pearce, blaming his departure on a "relationship breakdown" between the pair.
December 2007 - Sits out Newcastle's Boxing Day game through injury, but goes drinking in Liverpool city centre afterwards. In the early hours of December 27 he gets into a row in a McDonald's and violence again breaks out. Drunk, Barton straddles his victim, punching him repeatedly in the face. He is refused bail and is forced to spend the New Year behind bars.
May 2008 - Admits assault and affray and is jailed for six months, of which he serves 74 days at Strangeways prison in Manchester,
November 2008 - Escapes FA action after an on-pitch incident involving Aston Villa striker Gabriel Agbonlahor. Media reports claim Barton made a racial slur but Agbonlahor decides not to pursue disciplinary action.
May 2009 - Sent off on first game back from a long-term injury against Liverpool for a wild tackle on Xabi Alonso. Suspended by club following claims of a dressing-room row with manager Alan Shearer.
November 2010 - Backs controversial team-mate Andy Carroll for an England call, saying: "The frustrating thing for me is we pick the good guys, the guys who won't cause any problems. Hopefully England will stop worrying about what the sponsors are going to say and that 'goody two-shoes' is the right image for Team England. They need to start picking players to win football matches ... He can't be any worse than what's gone before."
November 2010 - Charged with violent conduct by the FA for apparently punching Blackburn's Morten Gamst Pedersen.