It has been announced Sajid Javid will take her place.
He is the first BAME (black, Asian or minority ethnic) politician to be given the job.
She resigned following a series of Home Office leaks to the Guardian, which revealed that information had been provided to her office about the targets.
He disowned the name of the "hostile environment" strategy, as Rudd had begun to do before she stood down, although not the policy itself. "This never should have been the case and I will do whatever it takes to put it right".
A day after losing one her most senior allies in cabinet, British Prime Minister Theresa May is attempting to stop the spread of the Windrush scandal to her own office.
"I was really concerned when I first started hearing and reading about some of the issues".
He said his parents, who migrated from Pakistan to the United Kingdom, would be incredibly proud of his appointment, before adding: "But I haven't called my mum yet".
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The SNP's home affairs spokeswoman Joanna Cherry said: "It is the prime minister who has created the fundamental reasons for the Windrush scandal".
Having been a strong supporter of Remain in the European Union referendum, she could now become a powerful voice on the Tory backbenches for a soft Brexit.
Rudd and May both apologized repeatedly, saying that all pre-1973 Commonwealth immigrants who don't already have British citizenship will get it and those affected will get compensation.
The newly appointed Home Secretary is the father of four children. "That is a huge responsibility, something I take very, very seriously". The crisis has unfolded rapidly over the past few weeks after it emerged that changes to Britain's immigration system had resulted in injustices to members of the Windrush generation - men and women largely from former British colonies in the Caribbean whose families had been encouraged to come to England to fill acute labour shortages before legislation in 1971 no longer gave Commonwealth nationals the right to remain in the UK.
Shortly after the appointment, Javid told the BBC his "most urgent task" was making sure the Windrush generation was "treated with the decency and the fairness that they deserve". The 48-year old, who previously served as business and culture secretaries, led the government's response to last year's Grenfell Tower fire disaster.
It forced a mini-reshuffle with James Brokenshire replacing Mr Javid as communities secretary, three months after he stepped down as Northern Ireland secretary to receive lung cancer treatment.
Melanie Dawes, MHCLG permanent secretary, on Twitter welcomed the new secretary of state to the department, and said it had been a pleasure to work with Javid.
Flanked by the foreign secretary, Boris Johnson, and the Cabinet Office minister, David Lidington, Javid said he was "personally committed" to rectifying the difficulties Commonwealth immigrants have had to deal with and would continue to resolve problems as a "matter of urgency".