His resignation comes after British Minister Theresa May undertook a reshuffle of her top team to reassert her authority after losing her parliamentary majority, in the election.
May's decision to keep them in their jobs was in part a reflection of her need to balance Brexit-backing ministers like Johnson and Davis with more pro-EU politicians such as Hammond and Rudd.
May is set to continue shuffling government ranks on Tuesday.
Several ministers may receive promotions, while a handful of MPs are anticipated to join the cabinet.
Meanwhile, the Financial Times, a British newspaper, reported on Monday, citing government sources, that the United Kingdom wanted to stay part of the European Medicines Agency after the body moves from London to Amsterdam.
The prime minister is likely to announce that a new ministerial position has been created to oversee preparations for the possibility of a no-deal Brexit.
May told the BBC in an interview broadcast Sunday that she hoped to secure agreement with the European Union on a post-Brexit transition period by March 31, and to draft a withdrawal agreement by the end of 2018.
"Damian Green's departure before Christmas means that some changes do have to be made, and I will be making some changes", she told a national newsbroadcaster.
David Lidington takes over at the Cabinet Office after Mr Green was forced out for lying over claims there was pornography on his office computer. So did Health SecretaryJeremy Hunt, a frequent target of criticism over failings in the state-funded National Health Service.
Henri Murison, the Northern Powerhouse Partnership's director, said: "It is vital that in key roles like Transport Secretary and Education Secretary, where opportunities like Northern Powerhouse Rail and improving our worst-performing secondary schools are critical, we see Secretaries of State prepared to unlock the funding and devolution of power needed to rebalance our economy for the long-term".
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.
Justice Minister Dominic Raab, an ardent Brexit supporter, is reported to be in line for a top job.
Downing Street said that as a result of the reshuffle there are now more women attending Cabinet, more female ministers and more members of the Government from a black and minority ethnic background than before.
The year ahead promises to be fraught for a prime minister who has lurched from crisis to crisis for months.
Grayling is a close ally of the Prime Minister, having been the campaign manager for May during her successful campaign to become the leader of the Conservative party.
She replied: "I've been asked that before and I've said, I'm not a quitter".