Pardew will serve an initial three-game stadium ban and will have to stay away from the touchline for an additional four matches, subject to an appeal.
The Magpies boss has also been fined 60,000 pounds and was given a warning about his future conduct by the FA.
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."
"As I have made clear, I deeply regret the incident and again wholeheartedly apologize to all parties for my conduct, which I understand was not acceptable," the club quotes Pardew as saying. "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 pounds and given a formal warning by the club following the incident during the Mapgies' 4-1 win against 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.
Chelsea boss Jose Mourinho defended Pardew following the incident, stating: "The problem is the human nature, and the human nature is open to mistakes. I made mistakes too. I paid for mistakes."
Meanwhile, Hull boss Steve Bruce praised Meyler as a 'model professional' after he scored in the Tigers' 3-0 FA Cup quarterfinal victory over Sunderland on Sunday.