Dame Martina has spent 14 years as chief executive of the Prince’s Trust and is also a non-executive director of the National Citizen Service.
And previously, she was chief executive of BBC Children in Need and of the Association of Spinal Injury Research, Rehabilitation and Reintegration.
The post of commission chair has been empty since December, when the previous occupant, Alan Milburn (no relation) resigned.
All four members of the commission resigned last year, following the publication of a damning report, which warned the UK in ‘the grip of a self-reinforcing spiral of ever-growing division’.
In his resignation letter to the prime minster, Mr Milburn said the government is ‘understandably focused on Brexit and does not seem to have the necessary bandwidth to ensure that the rhetoric of healing social division is matched with the reality’.
The education secretary, Damian Hinds,will now ask the chair of the education select committee, Robert Halfon, to arrange for the committee to meet Dame Martina.
Mr Halfon will consider the committee’s conclusions before deciding whether to proceed with the appointment.
Mr Hinds said: ‘Dame Martina has spent her career as a tireless champion for underprivileged children, young people and their families, providing better opportunities for them to fulfil their potential.
‘Her leadership of the Prince’s Trust has improved the education, skills and self-esteem of thousands of young people, and will be key in progressing our social mobility agenda.
‘I am grateful to her predecessor Alan Milburn, whose work as chair of the commission over five years shone a light on the injustices that still exist too frequently in this country. I look forward to working with Dame Martina as she works with us to eliminate them.’
Dame Martina added: ‘I hope my experience of working closely with and listening to young people from different backgrounds will help make a difference.’