Premier League clubs will have to prove they have at least four Covid-19 cases to get matches called off under new guidance announced on Wednesday.
A total of 22 top-flight games were postponed in December and January because of the pandemic.
The rules will be introduced before the next league fixture on 5 February.
A Premier League statement said the rules are designed "to protect the wellbeing of players and staff" and "maintain the sporting integrity".
Previously, clubs could request a match to be postponed if they did not have 13 available players as well as a goalkeeper.
However, teams were claiming opponents were including injured players as well as those on Africa Cup of Nations (Afcon) duty in Cameroon in the figures of players available.
Earlier this month, Tottenham said they were "extremely surprised" at the decision to call off their game against Arsenal, which had been scheduled to take place on 16 January.
However, the Gunners, who had four players at the Afcon tournament as well as a number of injuries and Covid cases, said they "reluctantly" requested a postponement and were "disappointed" the game had to be rearranged.
The Premier League said requests for postponements would continue to be assessed on "a case-by-case basis" and added: "Throughout the pandemic, the Premier League has adapted its guidance in response to the wider public health situation.
"The guidance was last updated in December in response to the emergence of the Omicron variant.
"The Premier League Board examines a number of factors, including the ability of a club to field a team; the status, severity and potential impact of Covid-19; and the ability of the players to safely prepare for and play the match."
A message on the scoreboard at Crystal Palace's Selhurst Park urging fans to wear a face covering
The league have said Covid passes will no longer be needed as a condition of entry to a Premier League match.
However, clubs have been urged to "follow public health guidance to keep each other safe on a matchday" and supporters should wear face masks when "indoors or in crowded areas" of the stadium.
Premier League chief executive Richard Masters said: "Fans have shown fantastic support for the measures in place and we thank them for helping keep each other safe and grounds open at full capacity.
"Despite Government restrictions easing, everyone still has a role to play in making sure people feel safe at our matches.
"We and our clubs urge supporters to continue to do all they can to follow public health guidance to minimise the risk of passing on Covid-19."
Simon Stone, BBC Sport
The reduction in the number of positive Covid-19 tests in the Premier League this week to 16, plus the increase in the number of Covid positives to four before a game can be called off, should have a significant impact on postponements.
The Premier League have always known postponing large numbers of games indefinitely was not an option because the final games have to be played on 22 May.
But the current international break offered the chance to re-assess and while injuries can still be used in proving a club cannot meet the 13+1 criteria, with the Africa Cup of Nations over before the next full round of matches, the international absences will not come into play again.
It should provide some certainty ahead of the next phase of the season, to the international window in March, in which there are seven rounds of matches, plus the fourth and fifth rounds of the FA Cup.
There are still 19 matches to be re-arranged, the four involving Leicester are particularly troublesome as Brendan Rodgers' side are about to embark on a Europa Conference League knockout campaign.
But the fact this new criteria comes into effect from the resumption should at least ensure the game that has caused most problems, the twice postponed relegation duel between Burnley and Watford, who now have a new manager in Roy Hodgson, should finally go ahead at Turf Moor on 5 February.