Sajid Javid has said his most "urgent task" is to help the Windrush generation, after succeeding Amber Rudd as home secretary.
The son of a Pakistani bus driver said he would review immigration policy to make sure it was fair and people were treated with "dignity and respect".
He is due to face MPs' questions on the subject in the Commons from 16:15 GMT.
Ms Rudd quit after she said she "inadvertently" misled MPs over immigration removal targets.
Ms Rudd told MPs last week the Home Office did not have targets for removing illegal immigrants, but on Sunday the Guardian published a letter 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.
When asked if she should take some personal responsibility for her home secretary's resignation, Mrs May said: "When I was home secretary, yes, there were targets in terms of removing people from the country who were here illegally.
"If you talk to members of the public they want to ensure we are dealing with people who are here illegally."
She said she was "very sorry" to see Ms Rudd go, adding: "I think she can look back with pride as home secretary."
Mr Javid, a former investment banker and MP for Bromsgrove since 2010, has been communities secretary for about 18 months.
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.
BBC political editor Laura Kuenssberg's view
Sajid Javid is not particularly a close ally of the prime minister herself.
He is not particularly an ardent Remainer – although his appointment retains the balance on the vital Brexit cabinet committee.
What he is, however, is someone who has already expressed public anger about the Windrush fiasco. He's also an experienced minister, who has been at several departments without major calamities.
However, he did face calls to stand down as business secretary over his response to the steel crisis in 2015 which saw Tata Steel cut thousands of jobs.
And he is also, as he sometimes jokes about with pride, a Conservative story of aspiration and hard work, a boy from an immigrant family who worked hard – and had a portrait of Margaret Thatcher in his office.
For him, challenges ahead are huge. But for him the opportunity is too.
- Read the full blog here
Windrush was the issue which led to change
Ms Rudd's departure came after she faced mounting criticism over her handling of the Windrush scandal and immigration policy.
The Windrush generation settled legally in post-war Britain and automatically got the right-to-remain in the UK – but the UK government did not keep a record of everyone in that position.
Some people who do not have the paperwork to prove they are in the UK legally have been detained, lost their jobs and denied access to medical care.
This has prompted calls for the government to abandon its "hostile environment" policy on illegal immigration, which Ms Rudd and Mrs May continued to defend.
Speaking shortly after his appointment, Mr Javid said he would be looking "very carefully" at existing policy.
"The most urgent task I have is to help those British citizens that came from the Caribbean the so-called Windrush generation and make sure that they are all treated with the decency and the fairness that they deserve," he said.
"I think that's what people want to see."
Mr Javid told the Sunday Telegraph over the weekend the Windrush scandal felt "very personal" to him as coming from a family of immigrants "it could have been me, my mum or my dad".
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Windrush immigration row
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The task ahead for new home secretary
The new home secretary faces a massive task. And none of it – from terrorism through to the Windrush crisis – is easy to fix, writes BBC home affairs correspondent Dominic Casciani.
The Home Office sits at the heart of some of the most complex and challenging decisions in government – and, if his predecessors' experiences are any guide, Sajid Javid should probably give up now on the hope of having much of a life beyond his red ministerial boxes.
First on the list for any incoming home secretary is appreciating the scale of the security threat.
Every day, he will see a dozen dossiers from the police and intelligence agencies asking for permission to intercept the communications of people who are a threat to the UK. This is his first responsibility: keeping the UK safe.
- Read Dominic's blog here.
Labour points finger at May
Labour shadow home secretary Diane Abbott said "all roads lead back" to Mrs May – Ms Rudd's predecessor at the Home Office – regarding the Windrush controversy.
She said the prime minister – the "architect of this crisis" – must come before the Commons to explain "whether she knew that Amber Rudd was misleading Parliament and the public last week".
"Many of the elements of this hostile environment originated under Theresa May and, most important of all, it was in 2014 that she passed legislation which removed the protection from deportation which up until then had applied to Commonwealth citizens," Ms Abbott told BBC One's Breakfast.
Following Mr Javid's promotion, No 10 also announced former Northern Ireland secretary James Brokenshire was returning to the cabinet as housing, communities and local government secretary while International Development Secretary Penny Mordaunt would take Ms Rudd's other role as women's and equalities minister.
How the immigration 'targets' row unfolded
When Ms Rudd was being grilled by a committee of MPs on Wednesday about the Windrush saga she told them there were no removals targets for illegal immigrants – comments subsequently contradicted by a 2015 inspection report.
She later admitted "local" targets for voluntary removals had been set but she 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 referred to targets. The newspaper also published a letter at the weekend, from January 2017, where Ms Rudd told Theresa May about plans to restructure her department and increase removals "over the next few years".
Sources told the BBC that on Saturday and Sunday Ms Rudd and her officials did a thorough search of all documents and found other references to operational targets which she felt she should have been aware of.
- Who are the Windrush generation?
- What is the 'hostile environment policy'?