Mrs May swiftly received backing from leading Brexit supporters Michael Gove and Boris Johnson, and the chairman of the Conservatives' backbench 1922 committee, Graham Brady, said there was no need for the leadership contest to be re-run.
And David Cameron said Mrs May will take the keys to No 10 by Wednesday evening.
READ : BREXIT is good news for Ghana, a nightmare for Ghanaians in Britain
Mr Cameron will chair his last Cabinet meeting tomorrow morning and appear in the Commons for the final time as premier when he takes to the Despatch Box for Prime Minister's Questions at noon on Wednesday.
Mrs May had launched her national campaign with a speech in Birmingham just moments before Mrs Leadsom's withdrawal today.