Taking over form Gauke, the new chief secretary to the Treasury will be Liz Truss.
The former education secretary, who clashed with Mrs May when both were ministers and was then sacked by her when she arrived in Downing Street, declared himself a "huge fan" of the PM.
Brexiteer Mr Gove becomes Environment Secretary and will have to deal with farming and fisheries as well as coping with flood disasters and implementing Tory policy to bring back fox hunting.
Green was previously secretary of state for work and pensions and is now expected to have a key role in supporting the prime minister and particularly in coordinating the negotiations for the UK's exit from the European Union.
Aside from Gove's appointment it appears unlikely that there will be further upheaval at the Department for the Environment, with Resources Minister Therese Coffey now in Italy for a G7 meeting on the Paris Agreement and George Eustice set to retain his role as Parliamentary Under Secretary of state for Farming, Food and the Marine Environment.
During his time as education secretary, Gove made plans to drop climate change from the geography curriculum, according to the Guardian, as part of a drive to slim the curriculum down.
After a tumultuous few days cobbling together a government with the DUP, and trying to persuade the country that she can continue to provide the "certainty" it needs going into Brexit negotiations, Theresa May on Sunday shuffled her cabinet. But what I'm doing now is actually getting on with the immediate job.
Within months of his sacking from the cabinet last year Gove was re-hired by the Times, writing columns and book reviews for a reported £150,000 a year. But I think that's what's important... Welcome back to Michael!
However Michael Gove, who left the Cabinet after a failed bid for the Conservative Party leadership previous year, has been appointed secretary of state at environment department Defra, replacing Andrea Leadsom.
But the prime minister said she had a busy schedule ahead, with a cabinet meeting on Monday and talks with French President Emmanuel Macron the following day.
Earlier, the Prime Minister announced she was promoting Damian Green to become First Secretary of State - a title associated in the past with the position of deputy prime minister.
May has faced criticism from within her own party for the decision to call an election and the manner in which she conducted the campaign.
Jeremy Wright carries on as Attorney General and Brandon Lewis remains a Home Office minister although he will in future attend Cabinet.