She also cleared out rivals, firing stalwarts of David Cameron's outgoing government including culture secretary John Whittingdale, education secretary Nicky Morgan and - most significantly - justice secretary Michael Gove, her onetime competitor for the job of Conservative leader.
After dropping out of the race to be PM, Mrs Leadsom has been made secretary of state for the environment, food and rural affairs.
Mr Davis has served as Foreign Office minister and shadow home secretary.
George Osborne, the chancellor of the Exchequer and a friend of Gove's, said in a speech of his own in Manchester on Friday that he would abandon his pledge to balance the budget by 2020, the end of this Parliament, because of the effect that the referendum would have on growth and the uncertainty surrounding it.
She was a passionate campaigner for Remain ahead of the European Union referendum and is now the second most powerful woman in Britain.
When it comes to candidates for Brexit minister, Sky's Jon Craig says potential candidates include Liam Fox, David Davis or even Andrea Leadsom, who could be in line for a Cabinet post in acknowledgment of her elevated profile following the Tory leadership contest.
Health Secretary Jeremy Hunt kept his job - despite his failure to solve the junior doctors crisis and reports that he too was on his way out.
After filling half-a-dozen of the top jobs Wednesday, Ms May made new appointments on Thursday, including justice secretary Liz Truss and education secretary Justine Greening.
There were also some resignations.
Work and Pensions Secretary Stephen Crabb has resigned from Government "in the best interests of my family".
As Justice Secretary he reversed many of predecessor Chris Grayling's policies including hated compulsory court fees.
Downing Street said that relevant civil servants will transfer from BIS to DfE as part of a change created to allow Ms Greening to "take a comprehensive, end-to-end view of skills and education, supporting people from early years through to postgraduate study and work". Her decisions will be talked about extensively and the history of her appointment can certainly be credited with reinvigorating a politically disinterested country. Like Mr Gove, she will combine the post with serving as Lord Chancellor.
It sounds as though Theresa May's meeting with George Osborne was one of the shorter ones ever known in this sort of setting.
In 2015, Johnson had to cancel planned public events in the West Bank because of security fears after he criticised backers of a boycott on Israeli goods, and he has previously described Hilary Clinton - US presidential hopeful - as having "a steely blue stare, like a sadistic nurse in a mental hospital". "I certainly want a European community where one can go off and scoff croissants, drink delicious coffee, learn foreign languages and generally make love to foreign women".
The chancellor also told Today the United Kingdom economy was entering "a new phase" because of the vote to leave the European Union, which he said had had a "chilling" short-term effect on the economy.
"That has shaken confidence, it has caused many businesses to pause investment decisions that they were making".
"Markets do need signals of reassurance, they need to know that we will do whatever is necessary to keep the economy on track", Hammond said. Mr Gove said that being a Cabinet minister for six years had been "an enormous privilege" and wished the new Government the "best of luck", while Mr Whittingdale wished his successor "every success".