The Prime Minister is carrying out talks in the devolved nations ahead of her promise to trigger Article 50 and formally start the process of withdrawing from the European Union by the end of the month.
It comes as Mrs May dismissed calls for a potential second independence referendum for Scotland before the Brexit deal is finalised.
She will be accompanied by Brexit Secretary David Davis and Welsh Secretary Alun Cairns, and will meet First Minister Carwyn Jones as well as leaders in business and other sectors.
It will also coincide with the signing of a £1.3 billion Swansea City Deal between the UK Government, local authorities and the Welsh Government, which aims to create more than 9,000 jobs in the region.
Speaking ahead of the visit, Mrs May said: "From my first day on the steps of Downing Street, I made clear my determination to strengthen and sustain the precious Union.
"I have also been clear that as we leave the European Union I will work to deliver a deal that works for the whole of the UK.
"I want every part of the United Kingdom to be able to make the most of the opportunities ahead and for Welsh businesses to benefit from the freest possible trade as part of a global trading nation."
Mr Jones welcomed the investment for Swansea as a "transformative deal" for the whole region.
"This is a package which will deliver jobs and economic growth for all of South West Wales, with clear benefits for all the areas involved," he said.
Additional reporting by Press Association