Greg Clark has been appointed to the newly created role of business, energy and industrial strategy secretary.
The former communities secretary will take control of the merged departments, with former business secretary Sajid Javid taking on Mr Clark’s previous role.
Chris Grayling will replace Patrick McLoughlin as transport secretary.
National media, camped outside Number 10 Downing Street, reported that Mr Grayling, the Conservative MP for Epsom and Ewell, has taken over the transport brief from Mr McLoughlin, who becomes Conservative Party chairman.
Justine Greening has replaced Nicky Morgan as education secretary in an expanded role, with skills and universities added to the Department for Education.
Ms Greening, a prominent anti-Heathrow expansion campaigner, will sit at Cabinet as education secretary and take responsibilities from the Department for Business, Innovation & Skills.
It is likely to mean the merger or scrapping of BIS, with speculation it may be merged with the Department of Energy & Climate Change or a new infrastructure super department may be created.
Following her appointments of key roles last night, including Philip Hammond as chancellor and Boris Johnson as foreign secretary, Mrs May is now appointing the rest of her Cabinet.
Education secretary Nicky Morgan and justice secretary Michael Gove have both been axed from their roles, after George Osborne was sacked as chancellor last night.
Stephen Crabb has resigned as work and pensions secretary.
Health secretary Jeremy Hunt stays in his post despite speculation he would depart, but Cabinet Office minister Oliver Letwin has been demoted.
Department of Business,— Christopher Hope (@christopherhope) July 14, 2016
Innovation and Skills, Department for Energy and Climate Change and Department for Transport are set to be closed.
They could be replaced with two new departments - one for— Christopher Hope (@christopherhope) July 14, 2016
Infrastructure and one for Industry, according to sources. #CabinetReshuffle
Liz Truss has been appointed as justice secretary.
Liam Fox was appointed as the new secretary for international trade last night.
Ms Morgan tweeted that she was “disappointed not to be continuing as Education Secretary & [Minister] for Women & Equalities – two wonderful roles it’s been a privilege to hold”.
Last night, the chancellor George Osborne tweeted it had been “a privilege to be chancellor these last six [years]”.
He said: “Others will judge – I hope I’ve left the economy in a better state than I found it.”
The chancellor told BBC Breakfast this morning that there would be no emergency Budget, despite warnings from his predecessor that it would be necessary in the aftermath of Brexit.
Big steer from Hammond on @BBCr4today that austerity will be put on hold - it was right in 2010, now in “a new phase”— dominic o’connell (@dominicoc) July 14, 2016
Speaking about Brexit, Mr Hammond said: “It came as a surprise to the markets… a surprise to business and therefore it’s rattled confidence. It’s caused people to put plans on hold while they wait to see how things clarify.”
Skills minister Nick Boles has lost his role, tweeting: “Theresa May will have my full support from the backbenches.”
Sky News senior political correspondent Beth Rigby tweeted speculation that Mrs May was looking to scrap or merge departments including BIS.
But ConservativeHome editor Paul Goodman said he had been told the Department of Energy & Climate Change would be folded into BIS.