The Department for Education and Skills said it was making the out-of-court settlement to cover the former Qualifications and Curriculum Authority chairman's lost earnings and legal costs, but did not accept his claims of unfair dismissal.
Former education secretary Estelle Morris sacked Sir William in September after schools claimed that the QCA had put pressure on exam boards to lower students' A-level grades to make them comparable to previous years.
Ms Morris said she had removed Sir William because of "a loss of confidence in the QCA which needs to be resolved". However, an inquiry into the exams fiasco, chaired by former chief schools' inspector Mike Tomlinson, found that Sir William had acted within the correct code of practice.
In a letter to Sir William, Charles Clarke, Education Secretary, said he valued his "distinguished service" to education over 14 years.
He praised Sir William's work on the new A-level system, saying he was certain Sir William had acted in good faith during the grading controversy to ensure that standards were maintained.
"I understand that the events of the autumn caused you and your family considerable public humiliation and great distress," the minister wrote.
"The circumstances which led to your departure were regrettable for all concerned and caused hurt to all parties.
"As someone with a warm regard for your considerable contribution to education over so many years, I certainly would not want the events of last autumn to detract from your record of public service."
Mr Clarke added that he hoped Sir William would continue to use his education expertise in a public role.