Here is a list of some of the main contenders to take big jobs in the May government, which reports suggest could include a new job of minister for Brexit:
Merkel expects Britain's May to 'quickly' define EU ties
Foreign minister under David Cameron, Hammond is tipped by some commentators to be May's finance minister.
An early supporter of May, Hammond, 60, is seen as a steady if unspectacular safe pair of hands.
Although he is seen as a eurosceptic, he backed the "Remain" campaign in last month's referendum which ended in a shock vote for Britain to leave the EU.
Finance minister Osborne is extremely close to Cameron and campaigned hard for Britain to stay in the EU.
Despite Cameron's resignation, the 45-year-old remains a powerful figure in the Conservative party and could get a role in May's Brexit cabinet.
He is thought to be hopeful of being appointed as foreign minister.
Grayling was May's campaign manager even though he backed Brexit while she opposed it.
May to become UK PM on Wednesday
His loyalty could be rewarded with a promotion from his current role as Commons leader, in charge of parliamentary business -- possibly to May's job as interior minister.
Grayling, 54, is another low-key operator considered unlikely to generate distracting headlines.
Leadsom was set to face May in the final round of the leadership contest but pulled out after a row over comments suggesting she was better placed to be leader as she was a mother, unlike May.
May could invite Leadsom, 53, a pro-Brexit figure whose leadership run won support from dozens of MPs, to join her cabinet as a gesture of unity.
Other anti-EU figures who could be brought in include current justice minister Michael Gove, who ran unsuccessfully for the leadership, and former mayor of London Boris Johnson, who sprung a surprise by not joining the race.
As energy minister under Cameron, Rudd was seen as efficient and reliable and she backed May early in the leadership contest.
Theresa May set to be next UK PM as Leadsom withdraws from race
Rudd, who helped recruit extras for the 1994 film "Four Weddings And A Funeral" in her youth, became an MP in 2010 after a career in finance.
The 52-year-old could be recruited as one of the leading female faces in the cabinet of what will be only Britain's second woman prime minister ever, after Margaret Thatcher.
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