Shadow home secretary Diane Abbott said Ms Rudd had "done the right thing".
Ms Abbott added that the "architect of this crisis" - the prime minister - must come before the Commons to explain "whether she knew that Amber Rudd was misleading Parliament and the public last week".
Ms Rudd, who was due to make a Commons statement on Monday, was under pressure to quit over the Windrush scandal.
The migrant community has been up in arms over the decision of the Home Office to deport Caribbean nationals who had been living in the UK for more than 50 years, under a new immigration policy.
Ms Rudd was forced to apologise for changes to immigration rules which she said had unintended and devastating impact on the Windrush generation who went to the UK in the 1940s and 50s.
Under the new rules, many immigrants lost their healthcare and jobs.
Ms Rudd said it had never been the intention for a crackdown on illegal immigration to affect those who were British in all but their legal status.
Ms Rudd has faced criticism over the existence of Home Office removals targets and her knowledge of them.
On Sunday, the Guardian newspaper published a letter to Prime Minister Theresa May, in which Ms Rudd set out her "ambitious but deliverable" aim to deport 10% more illegal immigrants over the "next few years."
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."
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