The bonus, on top of Mr Woodhead's senior civil service salary of about pounds 80,000 a year, was revealed after MPs on the Commons education select committee questioned Michael Bichard, Permanent Secretary at the Department for Education and Employment last month.
Don Foster, Liberal Democrat education spokesman, questioned Mr Bichard after publishing research questioning the link between school inspections and rising standards.
The committee, which will work out the inquiry's detailed terms of reference next month, is to seek evidence from some of the inspectorate's most vociferous critics in schools, local authorities and the academic world, as well as taking evidence from school inspectors and senior Ofsted figures.
The inquiry comes as Mr Woodhead moves towards the end of his contract, which expires next year. Ministers have yet to announce whether they intend to offer him another five-year term.
Ofsted has attracted huge controversy through its inspections of schools and teacher training colleges. Mere mention of Her Majesty's Chief Inspector of Schools can provoke booing at teacher union conferences.
Critics have questioned whether the inspectorate, which costs the taxpayer pounds 150m a year, offers good value for money. Research published earlier this year by the Liberal Democrats suggested Ofsted inspections made little or no impact on improving exam success. Inspectors are quick to refute criticisms, arguing that publishing inspection reports is central to raising school standards.
A spokeswoman for the National Union of Teachers said the union did not comment on officials' pay, but welcomed the select committee inquiry.
"It's something we have asked for," she said. "The Department should review Ofsted because there are questions about whether their mode of operations are supportive of schools or not. We have always argued that there should be self evaluation of schools, with targets set and Ofsted having reserve powers to inspect."
Ofsted has also angered the academic community, through its inspection of teacher training courses, and by its criticism of education research.
A spokesman for Ofsted declined to comment on individual salaries. He said: "The kind of targets Ofsted, and Chris Woodhead, has to meet is the completion of the four year cycle for inspections. Ofsted has met all its targets."Reuse content