Sir Nicholas will quit on 12 March, when he turns 60, a Revenue spokesman said. A successor will be announced shortly.
His decision to retire as chairman comes after much criticism in the past few years.
In 2001, the Inland Revenue decided to sell its 600-building estate to a company based in a tax haven.
The deal was made even more controversial by the fact that it was made without the knowledge of ministers.
He was under-fire again after a computer fiasco left thousands of low-income families waiting for their tax credit payments.
The Revenue board paid tribute to Montagu. In a statement it praised him ‘for the firm and clear leadership’ he had provided and noted that he had ‘transformed the role of chairman’.
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