She was one of 16 Labour party members made life peers last week, making Labour the largest party in the House of Lords for the first time.
Lady Morris became an education minister after Labour's election victory in 1997, rising to become school standards minister, then Education Secretary.
Lady Morris will be joined in the Lords by Gillian Shephard, who was Education Secretary from 1994 until 1997.
Lady Morris, a former teacher, was popular with teachers but resigned in 2002 after rows over criminal checks for teachers, the marking of A-levels, and the failure of 11-year-olds to meet test targets.
She announced last year that she would step down at the election after 13 years as MP for Birmingham Yardley. Labour lost the seat to the Liberal Democrats.
Lady Morris was recently appointed pro-vice-chancellor of Sunderland university, where she will examine how partnerships between schools and colleges can be improved.
She is to become chair of the Children's Workforce Development Council for England, which is responsible for ensuring that mentors, youth workers, early-years staff and education welfare officers are properly trained and work with each other.