Ms Rudd, who had been under pressure over what she knew about deportation targets for illegal immigrants, phoned Prime Minister Theresa May to tell her she was quitting.
She had faced intensifying calls to resign over claims she misled Parliament over the targets – as well as her handling of the Windrush scandal.
This has seen Commonwealth citizens who came to Britain after the Second World War being wrongly threatened with deportation.
In a letter to the PM, Ms Rudd said she “inadvertently misled” a committee of top MPs, adding: “Since appearing before the select committee, I have reviewed the advice I was given on this issue and become aware of information provided to my office which makes mention of targets.
“I should have been aware of this, and I take full responsibility for the fact that I was not.”
The PM said Ms Rudd had answered questions from the committee and MPs in the Commons “in good faith” and she was “very sorry” to see her leave.
Ms Rudd’s departure is a major blow for Mrs May, who publicly declared her “full confidence” in her ally as recently as Friday.
Having told the Home Affairs Select Committee on Wednesday that her department did not have targets for deporting illegal immigrants, a 2015 report swiftly emerged contradicting Ms Rudd’s evidence.
She was hauled before MPs and admitted they did exist. However, she claimed she was not aware of the targets and had not signed them off.
The pressure on the MP for Hastings and Rye increased further on Friday with the emergence of a memo – copied to her – which again discussed deportation targets.
Ms Rudd insisted once again that she did not know about them and claimed to have not read the memo.
Sky’s Political Editor Faisal Islam said: “My understanding is this is about what was and wasn’t said to Parliament rather than the handling in general of Windrush.
“If there’s some connection between a crackdown, which was certainly not aimed at the Windrush generation but in which they were caught up, then I think the Government may well have further questions to answer and clearly the opposition will try to point that towards Theresa May’s tenure at the Home Office.”
The resignation of Ms Rudd is the fourth Cabinet departure in six months, following the exits of Sir Michael Fallon, Priti Patel and Damian Green.
Labour’s Diane Abbott said the development was “inevitable” and should have happened “much sooner”.
The shadow home secretary said: “The architect of this crisis, Theresa May, must now step forward to give an immediate, full and honest account of how this inexcusable situation happened on her watch.
“Outstanding questions remain, and a change of Home Secretary must mean a change in the ‘hostile environment’ policies begun by her predecessor, or it will be meaningless.
“The Prime Minister must come before the House of Commons to explain whether she knew that Amber Rudd was misleading Parliament and the public last week about deportation targets.”
Liberal Democrat home affairs spokesman Sir Ed Davey said: “It’s clear that Amber Rudd has ended up, at least partly, being the fall guy to protect the Prime Minister.
“Theresa May must face questions now given these dreadful failures largely took place under her watch as Home Secretary.”
Labour MP David Lammy, who is the son of Windrush migrants, tweeted that Ms Rudd’s resignation “must not detract from the fact that this crisis was a direct result of the hostile environment policy” initiated when Mrs May was home secretary.
He called for the Home Office to quickly compensate and grant citizenship to the Windrush resignation.
Michael Gove paid tribute to his one-time Cabinet colleague, with the Environment Secretary tweeting: “I’m so sad about Amber’s departure from government – she was a huge asset – brave, principled, thoughtful, humane, considerate and always thinking of the impact of policy on the vulnerable – I hope Amber will be back soon – we need her.”
Backbench Tory MP Anna Soubry said Ms Rudd was a woman of “great courage and immense ability”, adding: “Amber will be missed in many ways. We’ll give her a huge welcome on to our back benches.
“If there is any justice she will soon return to the highest of office. Proud to call her my friend.”
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