Reuters
A prominent Brexit campaigner, Johnson was seen as the favorite to succeed David Cameron as prime minister before abruptly pulling out of the race earlier this month.
His role in Britain's negotiations over its future relationship with the EU is likely to be limited because May is expected to create a new ministerial post focused on Brexit.
Philip Hammond, who until earlier on Wednesday was Britain's Foreign Secretary, has succeeded George Osborne as finance minister in the government being formed by May to take Britain out of the European Union.
Hammond, 60, served as transport secretary when the Conservatives took power in coalition with the centrist Liberal Democrats in 2010, moving to take charge of defense in 2011.
His tenure as Foreign Secretary since 2014 has been dominated by the Ukraine crisis, Syria's civil war and negotiations that led last year to a six-power agreement with Iran to scale back its nuclear program.
Other confirmed cabinet ministers include conservative MPs Amber Rudd and Michael Fallon as UK home secretary and Minister of Defense, respectively.
Thomson Reuters
Britain's Foreign Secretary Philip Hammond listens to a journalist's questions during a news conference next to Mexico's Foreign Minister Claudia Ruiz Massieu in Mexico City
May, Britain's tough former interior minister, became prime minister on Wednesday, promising to champion social justice and rise to the challenge of leading the country out of the European Union.
The 59-year-old assumed office after an audience with Queen Elizabeth and drove straight to her new home of 10 Downing Street, vacated hours earlier by David Cameron, whose resignation after the vote to leave the EU brought her to power.
"We will rise to the challenge. As we leave the European Union we will forge a bold new positive role for ourselves in the world, and we will make Britain a country that works not for a privileged few, but for every one of us," she said.
Cameron stepped down after Britons rejected his entreaties to stay in the EU last month with a decision to get out that severely undermines European efforts to forge greater unity and creates economic uncertainty across the 28-nation bloc.
May must now try to limit the damage to British trade and investment as she renegotiates the country's ties with its 27 EU partners. She will also attempt to unite her divided Conservative party and a fractured nation in which many, on the evidence of the vote, feel angry with the political elite and left behind by the forces of globalization.
Reuters/Neil Hall
Theresa May emerges to speak to reporters after being confirmed as the leader of the Conservative Party and Britain's next Prime Minister outside the Houses of Parliament in Westminster, central London, July 11, 2016.
Acknowledging the struggles faced by many people, May declared: "The government I lead will be driven not be the interests of the privileged few, but by yours. We will do everything we can to give you more control over your lives."