May's decision to reshuffle her cabinet was a sign that she felt her internal position had improved enough to make some substantial changes to her top team without sparking a leadership crisis.
Mr Green - one of Mrs May's closest allies - was then fired from his position in December after making "misleading statements" to the press about pornography found on his office computer in 2008.
Health Secretary Jeremy Hunt has been tipped as a possible replacement.
Karen Bradley becomes Northern Ireland Secretary.
The most prominent Conservative ministers reportedly under threat are Education Secretary Justine Greening, Party Chairman Patrick McLoughlin, Business Secretary Greg Clark and House of Commons leader Andrew Leadsom, who May went toe-to-toe with in the final round of the party's 2017 leadership contest.
The Prime Minister offered Greening a job at the Department for Work and Pensions but failed in her attempt to keep the minister from quitting in protest at the move from education.
Although under pressure to differentiate her government from that of David Cameron's, May's new cabinet contains almost as many Oxbridge-educated ministers as that of her predecessor (50%).
Rightly have constitutional experts remarked that any Prime Minister's executive power over his or her colleagues is never more strikingly revealed than in a reshuffle.
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Chancellor of the Exchequer Philip Hammond, Brexit Secretary David Davis, Foreign Secretary Boris Johnson and Home Secretary Amber Rudd all stayed put - preserving a delicate balance of pro- and anti-EU voices that May navigates.
Beyond the hardcore mutineers, the ranks of disgruntled Tories have swollen since this week's reshuffle, joined not only by the ministers who were sacked but by those backbenchers who believed their hour was at hand, only to be overlooked when the time came.
"We're only now just getting into the wider part of the reshuffle", new Conservative party Chairman Brandon Lewis said on Tuesday in a BBC TV interview.
And Sajid Javid stayed in post but in the newly-named role of Secretary of State for Housing, Communities and Local Government.
Instead, immigration minister Brendan Lewis arrived at Number 10, a sure sign of promotion, followed by rising star James Cleverly. It is understood she turned down the Work and Pensions role.
May's reshuffle got off to a rough start when her Conservative Party's Twitter account announced the appointment of Chris Grayling as party chairman. Lidington will, however, likely take over Green's role in Brexit negotiations with the Scottish and Welsh governments. Penny Mordaunt continues as Secretary of State for International Development. "You could say that's an achievement after so many people wrote her off'".
While May's Cabinet is made up of fewer private-educated ministers than previous Tory governments, it is still way ahead of Labour PM Clement Attlee, who had just 25% of his 1945 Cabinet from fee-paying schools.
Caulfield led opposition to the campaign to decriminalise abortion past year, arguing that more consideration should be given to the rights of the unborn child.
