The 52-year-old, who had until 6pm on Thursday to respond to the charge, has requested a personal hearing, the date for which is due to be set.
An FA statement said: "Newcastle United manager Alan Pardew has admitted an FA misconduct charge in relation to his side's game against Hull City on March 1, 2014.
"Pardew was involved in an incident with a Hull City player in the 72nd minute of this fixture.
"Pardew has requested a personal hearing, the date of which will be set in due course."
Pardew was charged by the FA on Monday, two days after his latest touchline spat.
The Magpies were leading 3-1 at the KC Stadium and well on their way to a 4-1 Barclays Premier League victory when he and Meyler came into contact as the Tigers man chased a ball out of play close to the Newcastle manager's technical area.
Pardew reacted angrily and thrust his head towards Meyler's prompting an unsavoury melee.
Match referee Kevin Friend cautioned the player for his part in the incident and then sent Pardew to the stands, from where he watched the remainder of the game.
Pardew later issued a contrite apology, but his club responded within hours, warning him that his behaviour had been unacceptable and fining him £100,000.
That was the end of the matter as far as they were concerned, with sources on Tyneside quick to dismiss suggestions that the manager would be sacked as a result of his actions.
Humberside Police also decided there was no need for them to be involved, confirming there would be no criminal proceedings with neither Meyler nor Hull making a formal complaint.
However, that was never likely to be enough for the football authorities and, despite his guilty plea, Pardew seems certain to face stringent punishment.
His chequered recent history on the sideline - he has clashed with former Sunderland counterpart Martin O'Neill and Manchester City's Manuel Pellegrini, as well as pushing assistant referee Peter Kirkup - will not do him any favours, with the FA treating his latest offence as a "non-standard" misdemeanour.
It is understood a stadium ban, which would prevent him from watching his own team's games in person, is a distinct possibility.
Newcastle are not in action this weekend, but will resume at struggling Fulham next Saturday looking for a third successive victory.
Whether Pardew will be there or not remains to be seen, and assistant John Carver could find himself thrust into the limelight.
The Magpies currently sit in eighth place in the Premier League table, two points behind Manchester United and a further three adrift of the top six.
That is a significantly healthier position than the one in which they found themselves 12 months ago and they fought to retain their top-flight status, eventually finishing in 16th place with just 41 points, two fewer than they now have with 10 games still to play.