Greening's decision to quit came at the end of a long day of Cabinet meetings for the Prime Minister.
Mrs May's latest appointments included Alok Sharma who was given the role of Employment Minister, the role rejected by former Education Secretary Justine Greening.
Greening was succeeded as Education Secretary by Damian Hinds, who was promoted from being a junior Work and Pensions Minister.
The health secretary Jeremy Hunt, under pressure over a winter NHS crisis, refused to budge when he was asked to become business secretary, which is effectively a demotion.
And culture secretary Karen Bradley took on Brokenshire's Northern Ireland position, with digital minister Matt Hancock moving up to head DCMS.
Cabinet ministers are nearly over five times more likely to have gone to a fee-paying school compared to the general population.
A desire to maintain that equilibrium partly explains why the two men remained in their posts, despite criticism of Johnson's performance as foreign secretary and calls from hard-line exit supporters for Hammond to be fired.
HCS cancels school ahead of winter storm
A total ice accumulation of several hundredths of an inch is possible, according to the weather service. Localized gusty winds are possible and could produce blowing and drifting snow and reduced visibility.
A 'John Wick' TV Series Called 'The Continental' Is In The Works
Writer/producer Chris Collins (writer on The Wire , producer on Sons of Anarchy ) will be showrunner and write The Continental . Starz CEO and President Chris Albrecht said of the series, "This series is truly unlike anything else on TV".
Blue Jays avoid arbitration with OF Carrera and LHP Loup
A career.277 hitter, Donaldson has hit at least 29 home runs in each of the last four seasons. "I let my people handle it". Loup, who made $1,125,000 in 2017, went 2-3 with a 3.75 ERA in 70 appearances and 57 2/3 innings.
Following the ministerial changes, May said the reshuffle makes the government look "more like the country it serves" with a "new generation" of "fresh talent".
If this was the prime minister's goal, she failed here too, ignoring some of the party's rising stars such as Tom Tugendhat and Johnny Mercer altogether and moving others from positions where they shone to posts for which they are not obviously qualified.
And Jeremy Hunt and Sajid Javid had additional roles added to their titles, with the Health Secretary taking on responsibility for social care and the Communities and Local Government minister having housing added to his remit.
"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.
One minister who did leave the Cabinet was James Brokenshire, who resigned as secretary of state for Northern Ireland for medical reasons, telling May in a letter that he needed surgery to remove a small lesion in his right lung.
David Gauke leaves the Department for Work and Pensions to become the new Justice Secretary, replacing David Lidington.
It was later confirmed that Brandon Lewis, formerly immigration minister, was the new party chairman. However, they argued that she should remain in her role, citing a need for stability. Penny Mordaunt continues as Secretary of State for International Development.
Greg Clark stays as Business Secretary.
Baroness Evans of Bowes Park stays on as Lord Privy Seal and Leader of the House of Lords.