In her resignation letter Ms Rudd admitted that her office had been alerted to the targets and added: "I should have been aware of this and take full responsibility for the fact that I was not".
Three days after handing in her resignation as Home Secretary, Mrs Rudd took the opportunity to congratulate Sajid Javid MP for his promotion to the role.
As the Windrush scandal intensified, Rudd told a parliamentary committee the Home Office did not keep targets for the number of illegal immigrants removed from Britain.
On learning about the treatment of the post-war migrants, he said: "I thought that could be my mum.my dad.my uncle.it could be me".
'If you talk to members of the public they want to ensure that we are dealing with people who are here illegally, ' she said.
The new Home Secretary, the first person from a black, Asian or minority ethnic community to hold one of the great offices of state, said his background - he is the son of a bus driver who came from Pakistan in the 1960s - meant he was "personally committed" to resolving the problem.
Named after the British ship Empire Windrush, which arrived at Tilbury Docks in Essex with 492 Caribbean passengers in 1948, the Windrush immigrants never formalised their status, often because they were children who came over on their parents' passports and then never applied for their own.
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It follows the resignations of former defence secretary Sir Michael Fallon, Priti Patel as worldwide development secretary, Damian Green as first minister and James Brokenshire, who left his role as Northern Ireland secretary on health grounds.
On Sunday, in an interview with the UK's Sunday Telegraph, Javid said his family could have been caught up in the Windrush saga.
He is the the son of a Pakistani bus driver who immigrated to the United Kingdom in the 1960s, BBC reported.
"The last two weeks have seen an outpouring of sympathy and anger in response to the Windrush scandal, which has brought the daily cruelty of our immigration system out into the open".
Rudd then made a decision to resign rather than face the Commons on Monday, with her letter to May saying she had "become aware of information provided to my office which makes mention of targets. It is about a compliant environment and it is right that we have a compliant environment". Rudd later told Parliament that the Home Office did use local targets for internal performance management, but that she had been unaware of them.
Javid's appointment provides the Tory party with an opportunity for a reset on immigration - an issue which has dogged the government.