Ian Lang, president of the Board of Trade, and the Prime Minister have approved the appointment, and it is believed the only obstacle that remains is agreement of a leaving date with Mr Bridgeman's present employer.
The naming of a successor to Sir Bryan Carsberg, who left the post in May to become secretary-general of the International Accounting Standards Committee, had been expected some time ago.
It is understood that the announcement was delayed by the Conservative Party leadership election, with Michael Heseltine's departure from the Department of Trade and Industry only adding to the uncertainty.
Mr Bridgeman, 50, fits Mr Heseltine's known preference for a business person with an intellectual grasp of issues surrounding international competition policy to take on a role previously the preserve of lawyers, accountants and academics.
Sir Bryan Carsberg, the accountant who held the post until May, made no secret of the tensions between the office and the DTI under Mr Heseltine.
Last week, Sir Bryan said he had found a lack of government enthusiasm for competition policy, particularly at the DTI.
Observers believe Mr Heseltine favoured industrial competitiveness over strict competition criteria in a number of key cases, including the GEC bid for VSEL, the submarine builder, which was cleared after Sir Bryan's departure.
Mr Lang last week cleared the Scottish & Newcastle takeover bid for Courage, the brewers, with only cosmetic conditions attached.
Part of Mr Bridgeman's career of nearly 30 years at Alcan has been spent in strategic planning, and he is also a visiting professor of management at Keele University. Moreover, his membership of the Monopolies and Mergers Commission gives him experience of the other side of the competition business.
However, the desire to employ a prominent business figure is thought to have run into difficulty over salary because Sir Bryan earned about pounds 110,000 a year - considerably less than senior industrialists.
Although some in Government circles have suggested that the "less cash, more clout" argument offers a certain appeal, it is thought that the Government has got around the problem by increasing the package on offer.
Clare Spottiswoode, the gas regulator, has recently received a backdated 22 per cent increase to pounds 90,000 a year in recognition of the job becoming more time-consuming than was earlier envisaged.
Other senior public officials, such as Downing Street advisers, are reported to be paid about pounds 125,000.