Mr Gove's appointment as environment secretary just 11 months after the prime minister sacked him from the cabinet was the biggest surprise of Sunday's post-election reshuffle.
Green earlier served as work and pensions' secretary but being first secretary of state is the "deputy prime minister in all but name" title, reports the Guardian.
May revealed her cabinet this morning (13 June 2017) following Thursday's election, which resulted in a hung parliament.
Downing Street has also revealed that Liam Fox has retained his role as global trade secretary.
South Northamptonshire MP Andrea Leadsom has been made Lord President of the Council and Leader of the House of Commons.
The decision to keep her in the Government will be seen as an indication of Mrs May's weakness following the loss of her Commons majority in the General Election.
Although the role has has no formal powers, it is normally been held by top ranking cabinet ministers and confers some seniority over other secretaries of state.
Emmanuel Macron Confirms Third French Victim In London Terror Attack
He was known to security services and even featured in a television documentary entitled " The Jihadis Next Door ". Corriere wrote that Zaghba was stopped at Bologna airport in 2016 when he was trying to fly to Syria via Turkey.
May's Cabinet rehuffle follows last week's United Kingdom general election, which was created to strengthen the Government's hand ahead of Brexit negotiations.
"The Queen has been pleased to approve the appointment of Damian Green as first secretary of state and minister for the Cabinet Office", the statement read.
The DUP does not work or negotiate on Sundays for religious reasons, but officials from both sides are due to meet on Monday, and DUP leader Arlene Foster told Sky News she would meet May on Tuesday.
David Lidington takes charge as Lord Chancellor and justice minister and Alun Cairns as the new Secretary of State for Wales.
Gove was a key figure in the Brexit campaign, and took aim at European Union rules following the referendum which he said prevented homes being built.
"Liam Fox stays in his post as Secretary of State for worldwide trade, while Justine Greening has been re- confirmed as Secretary of State for Education".
His appointment has also been heavily criticised by political opponents and environmental campaigners, who say the former education and justice secretary is not up to the job.
Chris Grayling, who has been an MP for the past 16 years, will remain in the transport role he has held since July 2016.
No 10 said that James Brokenshire would be continuing as Northern Ireland Secretary.