Mrs May arrived at the palace by ministerial auto with husband Philip, having set off from the House of Commons only after receiving the signal that predecessor David Cameron's resignation as PM had been accepted by the Queen and that he had advised the head of state to appoint the former home secretary in his place.
Davis, a senior Conservative lawmaker who was beaten by former prime minister David Cameron in the party's 2005 leadership election contest, was appointed to the new role of Secretary of State for Exiting the European Union. If he were granted one wish, he said, it would be the "continued success of this great country that I love so very much".
Mr Cameron remarked that apart from a visit to Buckingham Palace to officially tender his resignation to the Queen, his diary was looking "remarkably light".
He emerged from the palace at around half past five.
Britain's new Prime Minister Theresa May (L) and her husband pose for photos in front of 10 Downing Street in London, Britain on July 13, 2016.
Theresa May became Britain's new prime minister on Wednesday, promising to carve out a bold new future in the world as she embarks on the monumental task of leading the country out of the European Union.
Late Wednesday it was learned she appointed Boris Johnson, leader of the Brexit forces, to the Foreign Secretary post.
She is under pressure - both from pro-Brexit Conservatives and other European Union leaders - to start formal exit talks with the bloc.
Cameron, 49, is the youngest prime minister to leave office since the Earl of Rosebery in 1895.
Standing with his wife Samantha and their three children, Cameron spoke of a legacy that includes legalizing same-sex marriage, investing in the National Health Service and giving aid to the poorest people and countries in the world.
Investors will be watching her first days in office closely but with greater optimism as the value of the pound, which fell by up to 15 percent against the dollar after the Brexit vote, rallied in recent days.
The Daily Telegraph said in an editorial that Cameron "leaves behind a stronger country, a thriving economy and more chances to get on in life".
"If you're from an ordinary working-class family, life is much harder than many people in Westminster realize", she said in a speech outside her new official residence at 10 Downing Street.
May did not specifically address Scotland's independence threat, but she promised to focus her efforts on creating a more equitable country that responds to the interests of those who feel left behind by politicians in London.
"In David Cameron, I follow in the footsteps of a great, modern prime minister". Her supporters say that, like the U.K.'s first female PM, Margaret Thatcher, May is steely and tough-minded.
Cameron announced his resignation as PM after the United Kingdom population voted "no" to remaining in the European Union by 52 percent to 48 percent in a June 23 referendum.
David Cameron revealed his advice to his successor Theresa May in one of his last acts as Prime Minister.
The Witney MP intends to continue as a backbencher but admitted he would miss the "roar of the crowd" and "the barbs from the opposition" that come with the top job in politics.
European Commission President Jean-Claude Juncker called on May to swiftly engage in divorce talks with the European Union.
Other prominent "Leave" campaigners were also rewarded alongside Johnson and Davis, including Liam Fox, named to head a new worldwide trade department.