Mr Montague, head of global project finance at the bank, will become chief executive of the Treasury's PFI Taskforce next month on a fixed salary of pounds 160,000. He will be on a two-year contract and will report to the Paymaster General, Geoffrey Robinson.
The 49-year-old banker, chosen from a shortlist of three candidates, described the job as a tremendous challenge: "You do have to feel a desire to help out in the public sector to hold a position of this type."
Mr Robinson, who dismissed Alastair Ross Goobey, the chairman of the Private Finance Panel, when Labour came into power, likened the job to a thicket through which Mr Montague would need to clear a path.
Mr Montague will recruit a team of around eight private sector project specialists and will have the responsibility of signing off commercially viable projects before they are put out to tender.