The home secretary Amber Rudd has resigned, saying she "inadvertently misled" MPs over targets for removing illegal immigrants.
Ms Rudd, who was due to make a Commons statement on Monday, was under pressure to quit over the Windrush scandal.
She faced criticism over the existence of Home Office removals targets and her knowledge of them.
Shadow Home Secretary Diane Abbott, who had repeatedly urged Ms Rudd to go, said she had "done the right thing".
On Sunday, the Guardian published the full letter it had reported on a week earlier, in which Ms Rudd set out her "ambitious but deliverable" aim to deport 10% more illegal immigrants over the "next few years" to Theresa May.
Ms Rudd telephoned the prime minister on Sunday evening to tell her of the decision amid intensifying opposition demands for her to quit.
A No 10 spokesman said: "The Prime Minister has tonight accepted the resignation of the Home Secretary."
Ms Rudd's successor will be announced on Monday morning.
The BBC's political editor, Laura Kuenssberg, said Ms Rudd resigned because "however inadvertently, it seems she misled parliament" and "officials couldn't guarantee there was nothing else that would have incriminated her still further".
The Windrush row began when it emerged that some migrants from Commonwealth countries, who settled in the UK from the late 1940s to the 1970s, and their relatives, had been declared illegal immigrants.
Reacting to the resignation, Labour MP David Lammy said: "Amber Rudd resigned because she didn't know what was going on in her own department and she had clearly lost the confidence of her own civil servants.
"The real issue is the hostile environment policy that caused this crisis in the first place.
"That policy must now be reviewed, and the Home Office must move quickly to compensate and grant citizenship to the Windush generation."
Im so sad about Ambers 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
— Michael Gove (@michaelgove) April 29, 2018
End of Twitter post by @michaelgove
How the 'targets' row unfolded:
- On Wednesday Ms Rudd told MPs investigating Windrush that there were no removals targets
- But an inspection report from December 2015 showed targets for voluntary removals did exist
- Ms Rudd then admitted "local" targets for voluntary removals had been set
- She told the Commons on Thursday she had not been aware of them
- The Guardian then reported a June 2017 memo from an official, copied to Ms Rudd, that refers to targets
- Ms Rudd said she had not seen this memo
- On Sunday evening, the Guardian published the full letter from Ms Rudd to Theresa May – which it had reported on a week earlier – setting out Ms Rudd's aims to increase enforced deportations
Giving evidence to the Home Affairs Select Committee last week, Ms Rudd said there were no removals targets for illegal immigrants.
She later admitted "local" targets for voluntary removals had been set, but told the Commons on Thursday she had not been aware of them.
But the Guardian reported a June 2017 memo from an official, copied to Ms Rudd, that refers to targets.
The newspaper also published a letter, from January 2017, where Ms Rudd tells Theresa May about plans to restructure her department.
She tells Mrs May – her predecessor as home secretary – that she plans to focus on the "aim of increasing the number of enforced removals by more than 10% over the next few years, something I believe is ambitious, but deliverable".
Ms Rudd's aim of increasing "enforced deportations" would not have affected Windrush migrants, as they were threatened with "voluntary departure".
The term "voluntary" describes the method of departure rather than the choice of whether or not to depart – those leaving in this way are able to approach the Home Office for financial assistance with travel costs.
Job made 'doubly difficult'
Analysis by BBC home affairs correspondent Danny Shaw
With responsibility for immigration, counter-terrorism and policing, the job of home secretary is one of the toughest in government. During one period under Labour, there were six home secretaries in eight years.
But Amber Rudd's job was made doubly difficult because she was following Theresa May, who'd survived in the post for more than six years and had set in train a series of plans and objectives that Ms Rudd was expected to stick to, even if she disagreed with them.
The former energy secretary was unable to put her stamp on any significant policy during her 21 months at the Home Office; much of her time was spent fire-fighting – dealing with the implications of Brexit, the rise in violent crime and last year's terror attacks.
Presentationally, Amber Rudd was impressive. But she lacked a command of the detail, which her predecessor had mastered, and it proved to be her undoing.