Former Education Secretary Charles Clarke replaced Mr Blunkett while David Miliband, school standards minister, took on Ms Kelly's post.
Mr Blunkett has been under fire for three weeks after allegations that he fast-tracked a visa for the nanny of his former lover, Kimberly Quinn.
Ms Kelly, a privately-educated mother of four, worked for three years in the Treasury before joining the Cabinet Office.
The daughter of a teacher, she numbers Margaret Thatcher among her role models and has risen to the Cabinet despite giving birth to her son and three daughters since she was elected MP for Bolton West in 1997.
Tipped as a future Labour leader, Ms Kelly is expected to back the Blairite agenda of choice in schools. Roth's Parliamentary Profile says she "believes state schools have to be made more attractive to the middle class".
Mary Bousted, Association of Teachers and Lecturers general secretary, described her as "a good Bolton girl and a person we will be able to do business with".