Arsene Wenger and Sir Alex Ferguson have promised to end their war of words ahead of the meeting between Arsenal and Manchester United on 1 February.
Arsenal vice-chairman David Dein and United chief executive David Gill vowed to ensure the dispute will end after a Premier League meeting on Thursday.
Premier League chief executive Richard Scudamore welcomed the announcement.
Scudamore said: "Public comments will be limited to pre-match and post-match analysis of the forthcoming fixture."
He added: "The board welcome the fact that both David Dein and David Gill arrived at the meeting having already received assurances from their managers that public comments on recent issues between them cease.
"The board is keen to stress that their concern related to the personal nature of recent exchanges and would never seek to restrict the huge interest generated for one of the season's most attractive fixtures.
"The board is grateful for the full cooperation of both clubs in this matter."
Football Association chairman Geoff Thompson had threatened to punish both clubs unless the feud ended.
"We're prepared to take whatever action is necessary to end hostilities between the clubs," Thompson told The Sun.
"I would prefer if it could be resolved internally. You don't want people wheeled into the headmaster's study."
Police have warned Wenger and Ferguson that their feud could create a public order risk when the two teams meet at Highbury next month.
Sports Minister Richard Caborn has also stepped into the debate, urging the managers to end the "pantomime" war of words.
The latest exchanges between Wenger and Ferguson date back to United's stormy 2-0 victory at Old Trafford in October.
"We were going to have a meeting with both clubs after the first game," said Thompson.
"We have responsibilities and we will make sure those are carried out. We want to try and resolve this issue."