The Magpies manager has been handed a lengthy suspension and a £60,000 fine by the FA, with the 52-year-old also subject to a three-match stadium ban as part of his punishment
Pardew will serve an initial three-game stadium ban and will have to stay away from the touchline for a further four matches, subject to an appeal.
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Newcastle released a statement on their official website stating: "The club and Pardew have accepted the decision and now wish to draw a line under the matter."
The club also quote Pardew as saying: "As I have made clear, I deeply regret the incident and again wholeheartedly apologise to all parties for my conduct, which I understand was not acceptable.
"I will accept the punishment handed down by the FA today. My focus now turns to preparing the team for this weekend's game against Fulham and finishing the season as strongly as possible."
Pardew was fined £100,00 and given a formal warning by the club following the incident during the Mapgies' 4-1 win over Hull on March 1.
Meyler and Pardew clashed as the Tigers player sought to retrieve a ball that had run off the pitch in the 72nd minute, with the Newcastle manager being sent to the stands by referee Kevin Friend after attacking Meyler.
Pardew will therefore be absent from the ground for Newcastle's upcoming fixtures against Fulham, Crystal Palace and Everton, and will not be allowed in the dugout for their clashes with Southampton, Manchester United, Stoke City and Swansea City.
He will be allowed back on the touchline for his side's trip to the Emirates Stadium to face Arsenal on April 28.
Pardew was given a two-game touchline ban last season for an altercation with an assistant referee, and was warned by the FA over his future conduct after a foul-mouthed tirade aimed at Manchester City boss Manuel Pellegrini in January.