May, previously the home secretary, won the race for leadership of the Conservative Party after her final rival, Energy Minister Andrea Leadsom, bowed out Monday.
Earlier Wednesday, Queen Elizabeth II officially accepted the resignation of outgoing Prime Minister David Cameron.
May, former home secretary, is Britain's second female prime minister after Margaret Thatcher, who ran the country between 1979 and 1990.
She acknowledged that Britain faces a rocky road ahead as it undoes 43 years of European Union ties and forges a new relationship with its neighbors.
"Following the referendum we face a time of great national change, " May said.
Mrs May said unionist meant preserving the "precious bond" between England, Scotland, Wales and Northern Ireland as well as fighting social injustice issues on behalf of minorities and the disadvantaged. When it comes to taxes we'll prioritize not the wealthy, but you.
She has begun to roll out new Cabinet appointments and has named Brexit campaigner Boris Johnson as Foreign Minister.
Britain has lacked a sense of direction since David Cameron announced his intention to step down and leaders of the Brexit campaign failed for various reasons to step up.
Philip Hammond, who had been Foreign Secretary, has succeeded George Osborne as Finance Minister, who has resigned.
He also reflected on the "spirit of service", which he said was "one of the most remarkable qualities" of the British character and praised the commitment of the armed forces and volunteers.
As David Cameron leaves office, public affection is thin on the ground with approval ratings at their lowest since he became prime minister in 2010.
"It has been the greatest honour of my life to serve our country as prime minister over these last six years and to serve as leader of my party for nearly 11 years", he said.
"It's not been an easy journey and of course we have not got every decision right, but I do believe that today our country is much stronger", Cameron said.
Then, he and his wife, Samantha, and his children - 12-year-old Nancy, 10-year-old Elwen and 5-year-old Florence - left their home of six years and made the short drive to Buckingham Palace.
Her visit was around 20 minutes after David Cameron went to the Palace to offer his resignation, with Samantha and their children in tow. He will now formally tender his resignation to Queen Elizabeth II later in the day and hand over to his successor, Theresa May. She has the tough task of calming the country and global financial markets after the upheaval that followed the referendum.
On a more serious note, Cameron said he cared passionately about the United Kingdom, adding that "we need to make sure as we leave the European Union, how we keep the benefits of the common travel area".
Not all believe her.
May has a daunting job as prime minister, facing pressure to start Brexit negotiations with the European Union, salvage a plummeting economy and unite a divided nation. But Tony Travers of the London School of Economics said May would likely not rush to trigger Article 50 of the European Union constitution, which starts a two-year countdown to a final exit. "I think she's a cautious person, and the British political establishment needs to come to terms with this massive decision".
Mr Cameron, who served as Prime Minister since 2010 and successfully retained office past year, resigned last month following the Brexit referendum in which just over 52 per cent of voters opted to leave the European Union.
Trying to reclaim his legacy from his Brexit miscalculation, Cameron said his government had cut the deficit, overseen economic growth and legalized same-sex marriage. "Amazing moments" Defending his economic, social and foreign affairs achievements, Mr Cameron said there had been "many fantastic moments" over the past six years of "public service in the national interest".
"I will miss the roar of the crowd, Cameron told Parliament".
But he used his last question period in the House of Commons to address a different controversy: claims that he has always hated Larry the cat, the furry resident of 10 Downing who famously likes to stroll in front of cameras camped outside the prime minister's official residence.
Bowing out yesterday, Cameron said: "Nothing is really impossible if you put your mind to it. I wish him the best of luck in all his future endeavours".
May was greeted with a huge cheer as she entered the House of Commons.