Measures such as the benefit cap, universal credit and personal independence payments would be rolled out under the proposals.
It comes after a long-running political row in the Northern Ireland Assembly, where welfare reform led to a stalemate in agreeing its budget.
While ministers said the measures would help get people back to work, Labour renewed their attack on the Government’s austerity agenda, calling it “a disastrous policy”.
Northern Ireland parties the SDLP and the DUP also clashed in the Commons as they rowed over what exactly had gone wrong to get to this stage.
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Westminster had to step in to draft the welfare legislation after a lack of consensus on the issue at the Assembly.
This followed a pact between Stomont’s two largest parties, the DUP and Sinn Fein.
These rows resurfaced when the SDLP’s Margaret Ritchie told MPs this legislation should have been set by the Assembly.
She added: “Devolution is damaged if the two largest parties in the Assembly and the Northern Ireland Executive pick and choose which powers they have and when they have them.
“I fear this could push people further into poverty.
“It is incumbent on the Government to ensure that people are protected, that there is some form of cushion.”
The DUP’s Sammy Wilson, though, said his party had acted to ward off “financial and political collapse” in the Assembly.
He accused the SDLP of taking “a totally irresponsible view” in blocking moves to pass welfare reforms at Stormont.
Mr Wilson also said this plan would mean the Government would continue to fund welfare payments, rather than these powers being funded by the Assembly’s block grant.
The MP for East Antrim said: “We were not delighted that the powers were taken away from us.
“But the ability to bring the legislation forward was blocked, and we then faced a situation where we could not bring forward our own bespoke Northern Ireland legislation.”
He also laughed off SDLP claims it had tried to lead a compromise, which he said consisted of pleading with Government that Northern Ireland was a special case for welfare reform.
“Baldrick couldn’t have devised a more stupid plan had he sought to do so,” said Mr Wilson.
Employment minister Damian Hinds said the measures were an important part of the Fresh Start agreement, and also gave the Assembly powers to make discretionary welfare payments.
Up to £585 million will be handed over via Northern Ireland Assembly’s block grant to make these payments to those worst hit by the changes.
Mr Hinds said: “Across the UK our welfare reforms are focused on supporting people to find and keep work, a focus on fairness, employment and affordability, whilst supporting the vulnerable.”
He added that raising the income tax threshold would take 110,000 people in Northern Ireland out of income tax altogether.
But David Anderson, shadow Northern Ireland secretary, said the higher rate of unemployment in Northern Ireland meant welfare reform would hit especially hard.
The Labour frontbencher added: “Welfare reform was intended by the Government to impact very, very hard on the most vulnerable people in the UK and force them into work, and when they’re not well equipped to do so.
“The desire to inflict on the people of Northern Ireland the same disastrous policy that’s blighted the lives of our constituents right across Great Britain is a desperate tactic by a Government more concerned with ideology rather than compassion.”
Tom Elliott, UUP MP for Fermanagh and South Tyrone, said: “There is a huge frustration, a huge frustration, that this has number one had to come back here to be implemented, but secondly that it has taken so long.
“At a huge cost to other departments, at a huge cost to departments like the health service and the education service where there have been delays after delays.
“And a lot of it has been just grandstanding.”
He added: “This could have been resolved many, many months, in fact years ago.
“And the delays have been at a huge cost to the people of Northern Ireland, the ordinary people who needed that healthcare and needed the education.”
He said he supported the Bill, adding that Northern Ireland “cannot get into this mess” again “otherwise the Northern Ireland Executive and Assembly will be back to a very, very difficult position and once again stalemate”.
Nigel Dodds, DUP MP for Belfast North, said that if Northern Ireland had voted against the welfare reforms it would have had to slash spending elsewhere such as health or education.
He said Sinn Fein and the SDLP had shirked their responsibility by trying to block the welfare cuts.
“The reality is had this measure not taken place, had the Fresh Start negotiations which took place primarily between the DUP and Sinn Fein not had a successful outcome, then we would have had full, untrammelled direct rule by now from this place.
“That is the reality of it.”
The Welfare Reform and Work (Northern Ireland) Order 2016 was approved by MPs.