Theresa May, 59, was confirmed as Britain's new prime minister on Wednesday after she accepted Queen Elizabeth II's invitation to form a government.
May became Britain's leader after Buckingham Palace said the queen was "graciously pleased to accept" David Cameron's resignation.
After her meeting with the queen, May returned to 10 Downing Street, the prime minister's official residence, to speak to reporters.
In his last speech before travelling to meet the queen at the palace, Cameron avoided mentioning Brexit and insisted he "leaves our country stronger."
"It's not been an easy journey and, of course, we've not got every decision right, but I believe we leave our country stronger," he said before the handover of power to May.
"It's been a privilege to serve the country that I love," he tweeted en route to the palace.
"I believe Theresa will provide strong and stable leadership," Cameron said in his speech.
In his final bow in parliament earlier Wednesday after six years as prime minister, Cameron said "I was the future once," echoing his 2005 comment to former Labour leader Tony Blair.
In a last prime minister's questions filled with jokes, laughter, tributes and farewells, Cameron told lawmakers from all parties that "you can achieve a lot of things in politics. You can get a lot of things done."
"Nothing is really impossible if you put your mind to it. After all, as I once said, I was the future once," he said.
In 2005, in a remark aimed at Blair in his first prime minister'squestions as opposition leader, Cameron said: "He was the future once."
Cameron resigned after he failed to convince a majority of voters in a June 23 referendum on EU membership to oppose leaving the political bloc.
May, In her acceptance speech on Monday, said Britain needs a "vision of a country that works for every one of us," after last month's Brexit referendum exposed social, economic and political divisions.
"Brexit means Brexit and we are going to make a success of it," said May, who had backed Cameron's Remain campaign before the referendum. But she faces mounting pressure to begin talks on Brexit with European Union officials sooner than she had planned.
May had advocated waiting until the end of this year to invoke Article 50 of the Lisbon Treaty, which sets the rules for a nation leaving the EU, but many British and EU politicians have urged her to move more quickly.
Much attention will now focus on what roles, if any, May hands prominent Brexit campaigners Andrea Leadsom, Boris Johnson, Michael Gove, Chris Grayling and Liam Fox in her new cabinet, amid speculation that one of those five could be given a new post of Brexit minister.
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