Mr Burnham came fourth in the Labour leadership contest and served as Secretary of State for Health in Gordon Brown's Government.
Previously he was culture secretary and chief secretary to the Treasury.
Four other shadow education ministers will serve on the Labour frontbench, but details of their ministerial briefs have yet to be confirmed.
Mr Miliband has chosen a large number of new MPs elected in the last general election to be promoted to shadow ministerial posts.
They include the new MP for Chesterfield, Toby Perkins, who in May won the seat from the Liberal Democrats with a 3.9 per cent swing, one of the largest gains for Labour in the country.
Sharon Hodgson, who was elected as MP for Washington and Sunderland West in May, was first elected as an MP in 2005 for a neighbouring constituency.
Ms Hodgson was a member of the children, schools and families select committee, and in 2008 she devised the Special Educational Needs (Information) Bill, which became law. She also called for pilots of universal free school meals.
The other two MPs named as shadow education ministers were ministers in the previous Government's Department for Children, School and Families.
Kevin Brennan, MP for Cardiff West, had served as an education minister and his last ministerial job was for FE, Skills, Apprenticeships and Consumer Affairs.
MP for Hartlepool Iain Wright became Parliamentary Under-secretary of State for 14-19 Reform and Apprenticeships in 2009.
