The meeting will see Britain's decision to leave the EU take centre stage, ahead of the formal negotiations with Brussels which are expected to begin next year.
May will meet with Scottish First Minister Nicola Sturgeon, Welsh FM Carwyn Jones and Northern Irish FM Arlene Foster and her deputy Martin McGuinness.
Sturgeon, leader of the secessionist Scottish National Party, has been the most vocal of the first ministers since the June 23 vote. Earlier this month she called for a fresh referendum on Scottish independence if Scotland's interests are not protected in the Brexit negotiations.
In a letter to May ahead of the meeting, Sturgeon called for each of the devolved parliaments to have the chance to vote on Brexit plans.
"I also endorse the proposal that the proposed negotiating package should be subject to a vote in each of the four of the United Kingdom's parliaments and assemblies," Sturgeon wrote.
Her Welsh counterpart Jones also pushed for such a vote in a separate letter to May, in which he also said all four UK parliaments should vote on the final deal with the EU.
May said Scotland, Wales and Northern Ireland will be able to participate in the plans through a new forum chaired by Brexit minister David Davis.
"The new forum I am offering will be the chance for them all to put forward their proposals on how to seize the opportunities presented by Brexit and deliver the democratic decision expressed by the people of the UK," May said ahead of the meeting.
Downing Street said the devolved governments would be able to put forward nominees to participate in the group, with plans to meet at least twice before the end of 2016.
Downing Street has not outlined its plans in detail but has hinted towards a "hard Brexit" which would see the UK leave the single market in order to have greater control over immigration.
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