Previous year sparked outrage amongst the British population after world football's governing body FIFA ruled that poppies were banned from being worn in football matches because they were too political.
Meanwhile, Wales and Northern Ireland were fined for displaying the emblem at their stadiums, the BBC reported.
The FA, SFA and FAW all lodged appeals, with the IFA not joining them only due to there being no right of appeal for fines below a certain threshold.
Once the new rules are agreed, players will be allowed to wear poppies on the pitch, but only on the conditions that the opposing team agrees and the competition organiser has no objection.
The new wording will have to be approved by a meeting of the International Football Association Board next month.
England captain Wayne Rooney wears a poppy on his sleeve.
Tracey Crouch, the United Kingdom's sports minister, was glad to hear Federation Internationale de Football Association is set to relax the rules on home nations displaying poppies.
Mrs May said there was a "clear message" from the House of Commons that "we want our players to be able to wear those poppies".
A hastily-arranged conference call next month of IFAB members - the body governing changes to the Laws - is expected to ratify the change in time for a potential commemoration of those that lost their lives in the Great War, as is traditional for England games in November.
The FA immediately said it would appeal against the Federation Internationale de Football Association disciplinary committee decision at the Court of Arbitration for Sport following last year's global matches, but that threat has now been dropped and it is understood those fines were never paid and will simply be forgotten.