Theresa May is promising to build a "better Britain" and to make the country's exit from the European Union, or Brexit, a success.
It comes after her only rival, Andrea Leadsom, unexpectedly withdrew from the race to become the ruling Conservative Party's next leader.
Speaking outside the British parliament, Theresa May says she is honoured and humbled to succeed David Cameron as prime minister.
"During this campaign, my case has been based on three things: first, the need for strong, proven leadership to steer us through what will be difficult and uncertain economic and political times, the need, of course, to negotiate the best deal for Britain in leaving the EU, and to forge a new role for ourselves in the world. Brexit* means Brexit, and we're going to make a success of it."
Mr Cameron, who announced his resignation in the wake of the country's referendum on the European Union, originally said he would stay on until September.
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But events have been brought forward after Ms May's only opponent, Andrea Leadsom, withdrew from the race to succeed him.
Theresa May was appointed the country's Home Secretary, or interior minister, after the Conservatives won the 2010 general election.
She has held the post for six years.
Ms May was originally against Britain leaving the European Union but has said there will be no second referendum on the issue.
German chancellor Angela Merkel says Britain needs to move quickly now.
"The United Kingdom will have to clarify quickly how it wants to shape its future relationship with the European Union. From a German perspective, I can only underline that Great Britain is an important partner, and we will remain closely connected to Great Britain in the future. But, of course, the EU and the remaining 27 member states also have to protect their interests. For example, whoever would like to have free access to the European internal markets will also have to accept all basic freedoms in return, including the free movement of people."
So far, Ms May has not said whether she believes the rights of EU citizens living in the United Kingdom should be protected.
Professor Anand Menon, from King's College in London, says Ms May's priority will be to deal with the aftermath of Britain's decision to leave the EU.
"In the current context -- uncertainty over Brexit, uncertainty over currency markets -- we need leadership, and one of the reasons we are having all this uncertainty is that we have essentially a lame duck** prime minister now. So I think people inside of government will be saying to her, 'Take over as soon as possible, and you can provide the leadership that is now lacking.'"
Meanwhile, Eurozone finance ministers have met in Brussels for the first time since the referendum.
EU Commissioner for Economic and Financial Affairs Pierre Moscovici says their position remains unchanged.
He says no negotiations with the United Kingdom will begin until the withdrawal process, or Article 50, is triggered.
"We should open the negotiations as fast, as quickly, as possible, because we need to limit uncertainty, which is not good for the economy. No negotiations at all should or could take place until the moment when the negotiation process is opened."
Exactly when Ms May will decide to do that is unclear.
