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.
St Michael man charged with murder of Tavon Alleyne
His sister, Tanella , also posted a photo of herself with Alleyne at the hospital, putting an emoji of an angel over his face. A man was arrested and charged with fatally shooting Rihanna's cousin in Barbados last week, according to local reports .
Saturday's Super 6 Picks: Chelsea To Beat Leicester At Stamford Bridge
Before I watched the Carabao Cup semi-final with Arsenal I would have said Chelsea would win this 3-0, but I'm not so sure now. Islam Slimani worked well in a mostly full strength Leicester side last time out, scoring two goals against Huddersfield Town.
United Nations report says Iran violated Yemen arms embargo
In November, the coalition tightened the blockade after the Huthis fired a missile into Saudi Arabia that was intercepted near Riyadh's worldwide airport.
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.