Mr Balls fills the vacancy left by Alan Budd when he stepped down after the last election.
The appointment - and particularly the fact that Mr Balls is to retain his special adviser status - has been condemned by the Tories, who have demanded that he give up his political role.
Since Labour came to power, Mr Balls has been the chancellor's closest and most trusted personal adviser on economic policy. He is married to the new health minister, Yvette Cooper, and worked closely with Mr Brown while Labour was in opposition.
Precedent
In the past, the chief economic adviser has generally been chosen from outside the Treasury, from the ranks of academic economists.
Former holders of the post have included Terence (now Lord) Burns, who went on to become permanent secretary to the Treasury.
The Shadow Chancellor, Francis Maude, said: "How can Mr Balls reconcile being chief economic adviser - a role in which he is supposed to give the chancellor impartial, accurate and credible advice on economic matters - with being a special adviser whose primary purpose is to serve the political interests of the Labour Party in government?
"This is yet another example of Labour ministers packing the traditionally neutral Civil Service with their party political henchmen.
"The appointment is covered in the stench of hypocrisy, cynicism and cronyism."
Unadvertised
The Liberal Democrat Treasury spokesman, Matthew Taylor, demanded to know why the post had not been openly advertised.
He said: "This is an extraordinary decision to promote Gordon Brown's closest political ally into an unadvertised, specially created Civil Service post.
"This can only be seen as a political appointment which undermines the principle of an impartial Civil Service."
An unnamed Treasury source said the appointment recognised "the reality of the central role that Ed plays in economic policy-making."
The Treasury press release said Mr Balls would "take an increased role on international issues following the Chancellor's appointment as the Chairman of the International Monetary and Financial Committee."
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