Speaking outside his new Downing Street office, Johnson -- who spearheaded the "Leave" campaign in the 2016 Brexit referendum -- promised to do a "new deal" with Brussels.
After being formally appointed by Queen Elizabeth II, Johnson set out his mission statement, insisting that the vote to leave the European Union must be respected.
"We will do a new deal. A better deal that will maximise the opportunities of Brexit," the 55-year-old said.
"I have every confidence that in 99 days' time we will have cracked it.
"The British people have had enough of waiting."
The new Conservative Party leader also made a raft of domestic policy announcements in a nearly 12-minute address.
"I will take personal responsibility for the change I want to see," he said, with his girlfriend Carrie Symonds watching with his team of aides.
"Never mind the backstop: the buck stops here," he said.
"If there is one thing that has really sapped the confidence of business, it is not the decisions we have taken -- it is our refusal to take decisions.
"Brexit was a fundamental decision by the British people that they wanted their laws made by people that they elected and that they can remove from office.
"We must now respect that decision," he said.
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