Many of former prime minister David Cameron's close associates were told by May that would not be offered a portfolio in her government on Thursday, which saw the biggest changes to the United Kingdom cabinet in more than six years.
White House spokesman John Earnest said the US congratulates May, and noted she is familiar to many in Washington. "I am not at all anxious about Boris Johnson, but... during the campaign he lied a lot to the British people and now it is he who has his back against the wall", foreign minister Ayrault said.
May has rung the changes in appointing her first 6 ministers, including the surprise nomination of Brexit campaign figurehead Boris Johnson as foreign secretary and other "Leave" campaigners filling posts.
She is now the 54th person and second woman to hold the office - after Margaret Thatcher - since it was created in the 18th century.
Gone, too, was Michael Gove, the justice secretary who many Tories believe betrayed former ally Johnson by running for Conservative leader himself - a job Johnson had long sought.
Others in line for significant roles include energy minister Amber Rudd, worldwide development minister Justine Greening, who recently came out as an openly gay minister, and home office minister Karen Bradley.
European Union leaders, still reeling from Britain's decision to become the first country to leave the bloc in its 60-year history, pressed May for a quick divorce.
May is something of an unknown quantity internationally, but European Council president Donald Tusk said he looked forward to a "fruitful working relationship" with her.
Foreign Secretary since 2014, Hammond, 60, has previously been Transport Secretary and was Defence Secretary for three years from 2011.
"The Prime Minister's legacy will undoubtedly be that he has taken us to the brink of being taken out of the European Union, so we will not be applauding his premiership on these benches", said Scots Nationalist MP Angus Robertson.
That is one explanation for the new Prime Minister's decision to hand this sensitive job to such an unsafe choice. Gove argued that Johnson was not up to the job. "Britain is open for business".
May is expected to name a raft of new ministers on Thursday.
He says it's clear the "upcoming negotiations will not be easy" but said it's "the responsibility of both sides to make the process of Britain's withdrawal as smooth as possible".
German Chancellor Angela Merkel said on Thursday that she spoke to May by phone late on Wednesday and invited her for talks in Berlin.
"His appointment will set the tone for talks with fellow European states, many of whom have been keen for Britain to move swiftly to begin formal talks, and have talked tough on the prospects of giving away access to the EU single market".
Still, Hardt suggests: "Britain remaining in the European Union should also be an option for the new government - it would be better for Great Britain and the rest of the European Union".
"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 just for a privileged few but for every one of us", May said, as her husband, Philip, stood nearby.
Hammond has been appointed Chancellor in Theresa May's first cabinet appointment.
Hammond acknowledged that the Brexit vote has had "a chilling effect" on investment, saying "the No. 1 challenge is to stabilize the economy, send signals of confidence about the future".