While Eurosceptic tabloids rejoiced, the Daily Mirror said Johnson's appointment left the kingdom's credibility "hanging by a thread".
May took over from David Cameron less than three weeks after Britain voted to leave the EU. She also spoke to U.S. President Barack Obama, underlining Britain's commitment to sustaining the countries' "special relationship" and partnership on intelligence-sharing.
Asked if Britain would launch the formal process of quitting the European Union by the end of this year, finance minister Hammond told LBC radio: "No, that's a decision that we haven't made yet".
European Parliament chief Martin Schulz is blasting the Cabinet picks of new British Prime Minister Theresa May as part of a "dangerously vicious cycle" that will hurt Britons in the long run.
May now faces the tough job of extricating Britain from its 43-year membership of the EU. She then became a Home Secretary since May 2010, which entitled her to be the longest serving Home Secretary in the past 100 years. The winning "Leave" campaign dismissed what it called "Project Fear", saying Britain would prosper if it regained independence from Brussels.
But she is facing economic and political challenges on a scale that few British politicians (with the possible exceptions of Gordon Brown, as prime minister, and Alistair Darling, as chancellor) have faced in decades.
That means two of the top four jobs in the government are held by women.
Johnson was the figurehead of the successful Leave campaign, but since the referendum had suffered widespread criticism and ridicule for failing to present a clear Brexit plan and swiftly dropping out of the leadership race.
No, Mrs. May, though a Conservative, is not an ideological stalwart of the right in the Margaret Thatcher mold.
Other ministers will be well known to their counterparts here too.
David Davis has been charged with leading the UK's exit from the EU. That will go to a dedicated "minister for Brexit".
A statement from Benjamin Netanyahu's office Wednesday said he sent a letter to May with his well-wishes.
But one senior Tory warned that May was "creating an army of disenchanted former ministers". He thanked him for "standing beside Israel, the good relations and the strengthening of ties" during his leadership.
On Thursday she followed up by removing the justice, education, culture and cabinet office ministers, an unusually high toll of sackings for a British cabinet shakeup.
New finance minister Philip Hammond signaled he would take a less aggressive approach to cutting the budget deficit than his predecessor George Osborne, who was dumped on Wednesday. Osborne has resigned from the government.
Jean-Claude Juncker, the European Commission President, urged her not to delay the start of the Brexit talks. "So I don't know what you're talking about".
"They both agreed that the strong collaboration between our countries should continue and the Taoiseach offered to visit London soon for talks on how they could best work together to achieve this", the spokeswoman added.
"May's radical reshuffle stuns the old guard", said The Guardian's front page, with headshots of the six women she has appointed to Cabinet posts.
Putting crucial global portfolios firmly in the hands of Brexit supporters was perhaps an astute move for Mrs May, who had argued for Britain to remain in the European Union.
She said that Britain will forge "a bold new positive role" in the world, outside of the European Union.
Its editorial, titled "May contain nuts", said the new Premier faced a difficult task in negotiating Brexit, but "instability at the heart of her Cabinet" caused by bringing in "several explosive egos... will make it harder still".