The development comes after Dominic Raab resigned from the post over the Brexit draft deal.
May's spokesperson confirmed the news while adding that Barclay would primarily work on getting the British Parliament's approval for the draft Brexit agreement, while May would take care of negotiations with the European Union.
Similarly, Amber Rudd was appointed as the work and pensions minister in place of Esther McVey who had also tendered in her resignation due to the draft Brexit deal recently agreed on by the UK and the EU.
May has strongly defended her draft deal amid calls for no-confidence and a flurry of resignations.
"This is a deal that delivers on the priorities of the British people," May told reporters at a press conference held after she presented the draft agreement to the British Parliament where Conservative MP Jacob Rees-Mogg launched a tirade against May while submitting a letter of no-confidence.
Around 21 Conservative MPs have called for May's ouster publicly, according to CNN.
The draft agreement includes 185 articles, 3 protocols, several annexes and is 585-pages long.
On June 23, 2016, citizens of the United Kingdom had voted to leave the EU after which the UK had formally notified the European Council of its exit by evoking Article 50 of the Lisbon Treaty on March 29, 2017.
The United Kingdom will leave the EU and all its institutions on March 29, 2019, and move into a 21-month transition period, according to the draft deal.