The arrangement, which may have helped the couple save more than £100,000 in tax, is similar to those recently criticised by the Prime Minister as a "problem" for the British economy.
The disclosure is set to embarrass the new Downing Street Head of Communications days after he was appointed as a "safe pair of hands" to replace Andy Coulson, the controversial former News of the World editor, in the £140,000-a-year post.
The little-known boss of the BBC World Service, Craig Oliver was the Prime Minister's surprise choice to take over the running of the Downing Street publicity machine last week.
A former editor of the BBC Ten O'Clock News, the 41-year-old has also held senior positions at ITV.
But it is his role helping to manage the finances of his more famous wife, Joanna Gosling, 40, that is now set to bring his appointment under scrutiny.
Last year Mr Cameron tried to justify his unpopular decision to increase capital gains tax by highlighting the problem of legal tax avoidance.
He said: "There is a problem at the moment. We are finding that a lot of people turn income into capital to evade the tax system, and we are losing about £1 billion because of that."
This kind of avoidance scheme is apparently what Mr Oliver has been running for his wife Miss Gosling, a regular presenter of Saturday evening and late edition's of the BBC Weekend News on BBC One and rolling news channel BBC News 24.
The couple, who have been married for 14 years, live in a £1.2 million house in Chiswick, west London, with their three young children. They brought the house for £862,000 in 2004 from Mark Pougatch, the sports presenter.
For the past five years Mr Oliver – whose annual BBC salary was between £60,000 and £100,000 – has also been paid a small salary to serve as company secretary of his wife's television company Paya Limited, through which her income as a freelance presenter is apparently paid.
The couple set up the company in 2005 with the help of accountant Nicholas Ridge whose firm specialises in helping clients, including television producers, "to make sure their tax bills are kept as low as possible".
Its accounts show that almost £150,000 a year has been paid into the "television and journalism" firm. If Miss Gosling earned this money on a PAYE basis she would have to pay around £52,000 a year in tax and National Insurance.
But paying it though the company transforms this income into "turnover" which can be used to cover various expenses, including such items as running a car and an office, and also paying her husband a salary of £2999.97.
Tax experts last week estimated the arrangement reduced Miss Gosling's annual income tax bill on the £150,000 of earnings to as low as £29,800 – which would amount to a saving of up to £22,000 a year, and potentially more than £100,000 since the firm was set up.
The tax savings are based on the firm's turnover up to 2008. After that the Olivers switched to making less-transparent "abbreviated" disclosures to Companies House, which are allowed for small firms.
But despite no longer showing the firm's income, its most recent filings for March 2010 disclose that it had more than £33,000 in cash in its bank account.
The Conservatives have previously been highly critical of the BBC for allowing its top presenters to class themselves as freelancers to avoid paying thousands of pounds in income tax.
Presenters including Jeremy Paxman, Fiona Bruce and Emily Maitlis set up service companies to channel their earnings, allowing them to make large savings on the amount of tax and national insurance they have to pay.
Critics say the BBC presenters do little work to justify their freelance status, as contractual restrictions bar many from working for other broadcasters or being paid for speeches in case they compromise their impartiality.
While in Opposition, Jeremy Hunt, now the Conservative Culture Secretary, criticised the arrangements, saying the freelance payments were BBC staff salaries "in all but name".
He added: "The BBC should be transparent about the salaries it pays, and it is not acceptable to hide that by paying someone as a freelance."
Number 10 sources said last night that the Prime Minister's comments about people avoiding tax were mainly aimed at very higher earners such as hedge fund managers.
In a statement released through Downing Street last night, Mr Oliver said: "The reason Joanna created a company is that she was told a number of years ago that the BBC was making it a condition of employment for freelance news presenters.
"I have not received a salary for the role of company secretary since the tax year 2007/8.
"I have already declared this to the Cabinet Office, and will relinquish the position of company secretary on taking up the post of Director of Communications."
A Whitehall source said that the "down side" of the employment arrangement which the BBC imposed on freelance presenters was that the presenters – including Mrs Oliver, who has had three children – received no maternity pay, sick leave, holiday pay or other benefits enjoyed by people employed on the BBC staff.
