The announcement comes a fortnight after David Davis abruptly quit his role as Brexit secretary over disagreements with May on her plan for a "soft" Brexit.
"I will lead the negotiations with the European Union, with the Secretary of State for Exiting the European Union deputizing on my behalf," May informed the parliament in a statement.
After the UK government agreed on the withdrawal plan earlier in July that envisions the creation of a free trade area, the EU-UK negotiations reached a deadlock.
The European Union claims that the UK proposal contradicts the EU guidelines on the integrity of the single market and urges London to go with the "backstop plan," which would keep Northern Ireland in the EU Customs Union.
The Brexit negotiations between London and the European Union began last year and are due to be finished by the end of March 2019.