Farage, 52, said he felt he had done all he could to achieve a vote for the United Kingdom to leave the EU in a referendum on June 23 and now he wanted "his life back".
May has been prime minister for nearly three years since she took over from David Cameron in the wake of the June 2016 Brexit referendum.
Britain is due to leave the European Union by October 31, with Johnson racing against time to strike a deal to meet that deadline.
The Conservative Party will form a minority government with the support of the Democratic Unionist Party of Northern Ireland
While Britain grapples with a hung parliament, EU has warned, 'We don't know when Brexit talks start. We know when they must end.'