Purnell resigned from the Cabinet last night in protest against Prime Minister Gordon Brown’s leadership.
The move, tipped by Money Marketing earlier this morning, will see Cooper become the eighth Work and Pensions Secretary in so many years.
Cicero Consulting director and chief corporate counsel Iain Anderson says: “Cooper has a good grasp of the whole economic policy piece.
“She is a formidable Commons performer and is very loyal to Gordon Brown. It is a choice you might expect.”
Purnell was preceded by Peter Hain, John Hutton, David Blunkett, Alan Johnson, Andrew Smith and Alistair Darling.
Prior to being Chief Secretary for the Treasury, Cooper was minister for housing and planning in the Department of Communities and Local Government.
The 40-year-old has also worked in the office of the deputy Prime Minister and the Lord Chancellor and held roles in the Health Department.
Universities Secretary John Denham, who served as a minister in the Department of Social Security, which preceded the DWP, was another potential contender for the role.
But it has just been announced he will replace Hazel Blears as Communities Secretary.
Cooper’s husband, Childrens’ Secretary Ed Balls, has missed out on the role of Chancellor.
Balls was widely tipped to replace Alistair Darling prior to Purnell’s shock departure but it has been confirmed that Darling will keep his job.