"My pitch is very simple. I'm Theresa May and I think I'm the best person to be prime minister of this country," May, who has been the UK's longest serving home secretary, said at a press conference.
She underlined that "Brexit means Brexit" as she announced that she will be running for party leadership contest, which is set to conclude by September 9.
"Our country needs strong proven leadership to negotiate the best possible terms for the UK leaving the EU. Brexit means Brexit. The campaign was fought, the vote was held, turnout was high and the public has given its verdict," the 59-year-old Conservative party leader said, adding, "We need leadership that can unite our party and our country".
May said that among her first jobs as the Prime Minister would be to create a new government department responsible for negotiating Britain's exit from the EU, headed by an MP who campaigned for Britain to leave the EU.
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May, considered as the most powerful Conservative woman since Margaret Thatcher, spoke about invoking Article 50, the formal procedure for leaving the EU, which Cameron has left for his successor to do.
"Article 50 should not be invoked before the end of the year," she said.
"I know I'm not a showy politician...I don't go drinking in Parliament's bars. I don't wear my heart on my sleeve, I just get on with the job in front of me and you can judge me by my record," May said.
Calling for an "open contest", she added: "Whether it's a woman or a man it's about the qualities of the people doing the job."
Seen as a tough politician for her firm stance on complex issues like immigration, May has strong support within the Conservative party.
Justice secretary Michael Gove, who was expected to back the leadership bid of fellow Brexit campaigner Johnson, has thrown his own hat in the ring instead.
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Others already in the race include work and pensions secretary Stephen Crabb and former defence secretary Liam Fox, making it a five-way contest so far. A short-list of two candidates will move forward to the final stages of party voting.
The party's executive committee has finalised the time-frame for the contest so that a new leader and PM is declared by September 9.