In a statement outside Downing Street, the 60-year-old premier promised to "fulfil the promise of Brexit".
It is said a deal has been worked out with Democratic Unionist Party which has won 10 seats to form a coalition government if permitted by the Queen. Instead, they lost seats and the majority, and will be forced to form a coalition government with a smaller party.
The alliance makes some modernizing Conservatives uneasy.
Any such arrangement would be fraught with political risk for May, fuelling uncertainty among businesses over what the final terms of Britain's departure from the European Union would look like, and how it will affect future trade with the bloc.
Corbyn's Labour Party officially backs Brexit. It is also not known if the other parties will be determined to obstruct her path, and come together to let Mr Corbyn - known to be on the left wing of Labour - lead a new government.
Gavin Barwell, a former housing minister, replaces joint chiefs of staff Nick Timothy and Fiona Hill. One of the standout figures in the General Election campaign has been the out leader of the Scottish Conservatives, Ruth Davidson, who led the Conservatives into second place in Scotland gaining 12 seats, including out MSP Ross Thomson in Aberdeen South. She vowed to take the country out of the EU's single market and customs union, essentially a free-trade zone, radically changing Britain's relationship with one of its biggest trading partners.
May said that "I want to reflect on the election and why it did not deliver the result I hoped for".
"Gavin will have an important role to play in that".
The party said Saturday that Nick Timothy and Fiona Hill have quit.
Predictions of Conservative success became more modest as the party's campaign faltered following a series of missteps.
A Prime Minister who is not able to pass legislation is most likely to find it more hard to get the best deal for Britain's future in the negotiations.
Prime Minister Theresa May called for a snap election earlier this year with expectations of boosting the Conservative's majority government but her party failed to secure the 326 seats needed to form another majority government.
No 10 has confirmed that Philip Hammond, Boris Johnson, David Davis, Amber Rudd and Michael Fallon will all keep their existing jobs as Chancellor, Foreign Secretary, Brexit Secretary, Home Secretary and Defence Secretary respectively.
After Thursday's vote, May's Conservative Party still has the largest number of lawmakers, but lacks a parliamentary majority.