May will host the first meeting of the Joint Ministerial Committee (JMC) since December 2014 on Monday.
They will "discuss how the administrations can work together to get the best deal for the UK and seize the opportunities that exiting the EU will bring", her Downing Street office said.
She will call on the devolved administrations to commit to working fully with the British government in a bid to enhance prosperity and security, Downing Street said in a statement.
While a majority in England and Wales voted for Britain to leave the European Union in the June referendum, a majority in Scotland and Northern Ireland voted for Britain's continued membership.
May wants to build "a new industrial strategy for the whole of the UK, to spread wealth, jobs and opportunity more evenly", Downing Street said.
"The UK government is resolute in its commitment to strengthening the union further and making a success of the opportunities ahead."
"Far more than mere geography brings us together -- and we are much more than the sum of our parts," said May.
"As we move into this new chapter, we must seize the opportunities ahead, as we will achieve far more together than we could ever do apart.
"I want Monday's meeting to be the start of a new grown up relationship between the devolved administrations and the UK government -- one in which we all work together to forge the future for everyone in the United Kingdom."
Heading into the JMC, the Scottish government's Brexit spokesman said Edinburgh should be treated as an equal partner in the EU exit negotiations.
"We have yet to see a proposal from the UK government on how the views of people in Scotland will be taken into account," he said.
Sturgeon's left-wing secessionist Scottish National Party, which runs a minority devolved government in Scotland, has drawn up draft legislation for a second referendum on independence.
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