Foreign Office Minister Sir Alan Duncan labelled Boris as an "utter wimp" who couldn't stand up to US President Donald Trump's twitter storm.
Kim Darroch said in a letter Wednesday that even though his posting was due to end this year, he believed "in the current circumstances the responsible course is to allow the appointment of a new ambassador".
Darroch said he is "grateful to all those in the United Kingdom and the USA who have offered their support during these hard few days".
Memos from Kim Darroch in which he described the Trump administration as inept were leaked to a British Sunday newspaper, infuriating the USA president, who launched a Twitter attack on both the envoy and outgoing British Prime Minister Theresa May.
"Somebody has, for whatever malicious reasons, sought to either damage the UK-US relationship or indeed Sir Kim personally", British trade minister Liam Fox told reporters.
As the spat between the two allies intensified, Trump said he would no longer deal with the "very stupid" Darroch and called May "foolish".
As I understand it, many of ambassador Sir Kim Darroch's personal staff were in tears this morning.
Diplomatic memos he had written were released earlier this week questioning whether the White House "will ever look competent" under Mr Trump and referring to its "incoherent, chaotic" foreign policies.
"We don't really believe this Administration is going to become substantially more normal; less dysfunctional; less unpredictable; less faction-riven; less diplomatically clumsy and inept", Darroch wrote in one cable.
While May gave her full backing to Darroch, her potential replacement as prime minister, Borish Johnson, declined to explicitly support the diplomat and instead emphasized the need for maintaining good ties with Washington.
"I wouldn't use the language President Trump used, and I wouldn't agree with it", he said.
He had been Britain's top diplomat in Washington since 2016, predating Trump's presidency.
Darroch, who said his position had become untenable, had watched the debate, a diplomatic source told Reuters and another source familiar with the envoy's thinking said the former London mayor's comments "were a factor" in his decision to resign.
"I don't think he got the support he needed from across our political class".
Mr. Johnson has a close relationship with Mr. Trump and the U.S. President has spoken highly of him.
Downing Street said yesterday that officials had held "initial discussions" with the police about whether the leak inquiry could become a criminal investigation.
Appointing ambassadors usually involves a formal civil service process with advertisements, applications and interviews, though Simon McDonald, head of Britain's diplomatic service, said the post of ambassador to the United States wasn't always chosen that way.
In his statement he revealed that he wanted to "put an end" to the speculation around his future following the furore over the leaking of the damaging secret memos.
The First Minister of Scotland Nicola Sturgeon tweeted that it was "shameful" the diplomat had "effectively been forced out".