Although the government insists it has not backed down, the deal comes months after Tony Blair declared that the review bodies' terms of reference had been changed unilaterally in the national interest.
Under the initial changes, Tony Blair set out a four-point framework for the review bodies covering health workers, teachers, top civil servants and the armed forces.
Those changes, requiring the review bodies to work within departmental spending limits and the government's inflation target, were challenged not only by public sector unions but also by the review bodies.
One change states that the review bodies are 'independent' and 'make recommendations to the prime minister', instead of merely 'adivse'.
Mr Milburn said: 'We have been able to finalise the remit for both the review bodies which confirms their independence and makes clear the criteria that they need to take fully into account when making recommendations.'
Bob Abberley, head of health for Unison, welcomed the government's 'small but significant step back' from undermining the independence of the review bodies.