The plan is expected to create more than 9,000 jobs and trigger almost £1.3bn investment in the region.
Mrs May said it would "benefit the whole of Wales".
It comes as First Minister Carwyn Jones told the Guardian Mrs May had a "tin ear" on issues of devolution.
Downing Street said Mrs May's visits to the four UK nations, which begin in Wales, would ensure the government was "engaging and listening to people from right across the nation" before triggering Article 50 to leave the European Union.
Q&A: What is in the Swansea Bay city deal?
Speaking ahead of the city deal signing, the prime minister said: "Wales' universities already have an excellent international reputation.
"They attract overseas students and pioneer in research projects here and abroad.
"I also want Wales to be at the forefront of science and innovation, as demonstrated by today's landmark city deal for Swansea.
"The deal is a great example of what can be achieved when the UK Government, the Welsh Government and local authorities work together to secure a deal that benefits the city and the whole of Wales."
As well as meeting the first minister, Mrs May will see representatives from a range of sectors and businesses at the signing ceremony at Swansea's Liberty Stadium.
Speaking ahead of the signing, Mr Jones said:  "We have pushed long and hard for this city deal to be signed and have given it our strongest possible backing with £125m of Welsh Government investment.
"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.
"Today's announcement is a transformative deal that will drive the regional economy in a new direction, supported by high-quality jobs and a digital infrastructure."
Rob Stewart, leader of Swansea council and the city region, said: "This is among the biggest investments Wales has ever seen, so it's a historic day for the Swansea Bay City Region."
Prime Minister Theresa May will sign off the Swansea Bay City Region deal later, insisting she wants Wales "at the forefront of science and innovation".