Earlier Wednesday, Queen Elizabeth II officially accepted the resignation of outgoing Prime Minister David Cameron.
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Speaking outside her new home, 10 Downing Street, May delivered a message directed at the British population from all walks of life.
Cameron announced his resignation last month, following the UK’s shock referendum result to leave the EU.
Mrs May suddenly won the Conservative leadership contest after rival candidate Andrea Leadsom pulled out on Monday.
A career politician, Theresa May is the first woman to hold the office since Margaret Thatcher in 1990.
She was formally appointed PM after a half-hour meeting with the Queen in Buckingham Palace and is expected to unveil the first members of her cabinet later on Wednesday.
In his farewell statement outside Downing Street, Mr Cameron said Mrs May would provide “strong and stable leadership” and wished her well in her negotiations on Britain’s exit from the EU.
May pledged to fight burning injustices saying: “We must make Britain a country that works for everyone”.
Just minutes after being invited by the Queen to form a Government, the new Prime Minister stressed her determination to preserve the Union between England, Scotland, Wales and Northern Ireland.
Cameron had called the referendum and campaigned to stay in the European Union in a bid to try to heal divisions in his Conservative party.
In his emotional final address to the country, Mr Cameron said that he believed he was leaving the country “much stronger” and the economy “immeasurably stronger” after his six years in office.
On leaving the prime minister’s Downing Street office, Johnson immediately got into a ministerial auto and went to speak to staff at the Foreign Office.
Cameron said it was the “greatest honour” of his life to serve as prime minister. She seems intent on using such appointments to help chart a different course than that of Cameron.
In his last moments in the post, Cameron said that serving as prime minister was “the greatest honor of my life” in a speech in front of the Downing St. residence, flanked by his family.
“I came into Downing Street to confront our problems as a country and lead people through hard decisions so that together we could reach better times”, Cameron told the Telegraph in an article published Wednesday. The warmth culminated in a standing ovation for Cameron, 49, who is leaving office after voters rejected his advice and made a decision to leave the European Union.
“Following the referendum, we face a time of great national change and I know because we are Great Britain, we will rise to the challenge”, May said outside the prime minister’s Downing Street office.
In a surprise appointment, May named Boris Johnson, the former London mayor who became a fiery advocate of the Brexit campaign as foreign secretary.
Earlier Wednesday Cameron performed his final official duty at Prime Minister’s Question Time in the House of Commons, earning warm praise from all sides of the house, including from his main adversary, Jeremy Corbyn, leader of main opposition Labour Party.
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After warm tributes from MPs from all parties, Mr Cameron ended his farewell by telling the Commons: “I was the future once”.
