Ms Downs, who has headed the council since 2003, becomes deputy permanent secretary and director general of the corporate performance group.
She will take up the post early next year - on 1 April 2009 the six Shropshire councils will merge to make one new council delivering services for the whole county.
Ms Downs has 26 years' experience in local government - 18 years in a senior management role and more recently at the helm in Shropshire, which was recently declared as the best performing county council in the country.
Suma Chakrabarti, Ministry of Justice Permanent Secretary, said: "I am delighted that Carolyn will be joining my senior team, given her track record in Shropshire.
"She is currently one of our Non-Executive Directors and I have had the chance to see first hand the added value she brings."
Ms Downs said: "I am very excited about taking up this role and thrilled to have the opportunity to contribute further to the work of the Ministry of Justice and the wider Civil Service.
"I am looking forward to working with people across the organisation."