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Stephen Crabb will take over from Iain Duncan Smith at the Department for Work and Pensions, David Cameron has announced.
Crabb, the MP for Preseli Pembrokeshire and former Welsh Secretary, was appointed in the wake of Duncan Smith's surprise resignation over proposed cuts to disability benefits, which sparked an emergency reshuffle of the cabinet.
Glamorgan MP Alun Cairns has been selected as the new Welsh Secretary, while Aberconwy MP Guto Bebb has been appointed as Parliamentary Under Secretary of State at the Wales Office and a Government Whip.
Defence secretary Michael Fallon has described the resignation of work and pensions secretary Iain Duncan Smith as "puzzling".
Mr Fallon said Duncan Smith's departure was "disappointing", but added work to make the benefit system simpler and fairer "will go on".
Mr Fallon admitted current proposals to cut disability benefit require more time.
But he added that the Government's general Budget proposals, which Duncan Smith claims favour higher earners, "benefit everybody, not just the wealthy".
Tory MP Peter Bone says he wasn't surprised to hear that work and pensions secretary Iain Duncan Smith had resigned over the extent of proposed disability cuts as he is a "man of principle".
Speaking to ITV News, Mr Bone said he believed his fellow MP had left because of the "roadblock" presented by the treasury that had stopped him from being able to conduct himself in his aim to sort the welfare and benefit system out.
In a statement, Mr Bone said:
Downing Street has told ITV's Political Editor Robert Peston that its 'current version' of proposed disability cuts will not go ahead.
It comes after the Chancellor's plans for a £1.3 billion a year cut in disability benefits was met with fierce opposition, including from within his own party, and even led to the resignation of work and pensions secretary Iain Duncan Smith earlier this evening.
The Labour leader Jeremy Corbyn said said that Iain Duncan Smith's shock resignation has revealed a government in disarray over cuts to welfare.
He said that chancellor George Osborne has lost credibility with the British public and should also step down over the row.
Iain Duncan Smith worked 'tirelessly' to hep those on welfare, a Conservative MP has said after the work and pensions secretary resigned over the extent of cuts.
Andrew Percy suggested that the latest round of cuts - including controversial curbs to disability payments - may have been forced on the department by Downing Street in comments to BBC News.
Nicola Sturgeon, the leader of the SNP and first minister of Scotland, has called for the government to immediately reverse planned cuts to disability benefits in the wake of Iain Duncan Smith's resignation.
Ms Sturgeon said the decision of the work and pensions secretary to quit in protest showed the need for a "fundamental rethink" on the Conservative Party's welfare policy.
Latest ITV News reports
Iain Duncan Smith tells ITV News' Robert Peston his resignation was intended to push the government into pursuing a fairer welfare policy.
Former Work and Pensions Security accuses government of making 'arbitrary cuts' which he says damages the party and the country.