The co-presenter of maths quiz show Countdown and mental arithmetic whizz is to be the "face" of the year of mathematics - which begins in 2000. Mr Blair will announce his coup on Tuesday.
Ms Vorderman, a Cambridge engineering graduate, has been recruited to make maths more user-friendly. But her appointment seems set to raise accusations of a conflict of interest because of her association with the Tokyo-based Kumon Institute of Education, a private company with a worldwide network.
The fee-charging Institute provides after-school maths tuition employing traditional rote-learning methods. Millions of parents have enthused about its methods, but maths teachers have been more critical, claiming it stifles understanding.
Ms Vorderman's six-year old daughter Katie attends Kumon classes. The presenter also appears on a publicity leaflet for the Institute.
The Government is almost certain to be accused of identifying itself with the Kumon Institute, providing it with priceless free advertising.
As part of her government job, Ms Vorderman will encourage parents to brush up their times tables with puzzles and engaging maths quizzes, while children under eight will be banned from using calculators at school. The drive will also target those without basic adding and subtracting skills so that they can feel confident about counting change in shops and checking that their telephone bills are correct.
Ms Vorderman, who has an IQ of 157 and is a member of Mensa, has held meetings with the Prime Minister over the past months about fronting the project. She is a keen proponent of mental arithmetic, and produces maths videos for children.
The television star, who used to present Tomorrow's World, recently signed a pounds 5m contract with Channel Four to co-present Countdown,where she solves mental arithmetic puzzles. The quiz show, which has 4 million viewers a day, was recently embroiled in controversy when the political columnist Matthew Parris revealed that guests receive help from backstage through an earpiece.
Ms Vorderman, dubbed "telly brainbox" by the tabloids, does all the sums herself and has a 90 per cent success rate. But when she was recently caught out by a difficult sum on Countdown, her mistake hit the headlines. She failed to calculate 959 using 75,2,9,1,10 and 4.
Ms Vorderman, who earns more than Cilla Black and Judy Finnigan of This Morning, attributes her maths skills to good mental arithmetic training at primary school.
The Government wants to give the maths initiative a popular face. The cast of the soapopera Brookside helped endorse the year of reading and the soap has run a storyline about literacy recently.
The Government intends to put around pounds 20m into Maths Year 2000 which will involve a new framework in schools for teaching maths.
The year is to mirror the Year of Reading which has led to big improvements in exam results where the scheme has been piloted.
Last year the Prime Minister appeared on the radio to endorse the year of reading, and spoke of how he read to his own children. But his ministers have been caught out in the past by their inability to do sums.
Stephen Byers, now the Trade and Industry Secretary, appeared on Radio Five Live when he was Education Minister and incorrectly said that 8 x 7 was 54. Later the same day, Education Secretary David Blunkett was asked what 9 x 8 was at a press conference. He correctly answered 72 - after a brief hesitation. Ministers are likely to be told to brush up their times tables to avoid an embarrassing repeat of the Byers gaffe.
On Tuesday the Prime Minister will launch the maths year with Carol Vorderman, David Blunkett and assorted educationalists. They will try to stress that boasting about being bad at maths is unhelpful to young people at school. The Prime Minister is expected to say that too many people are quick to dismiss the need to learn basic maths skills.
He will add that with the national year of reading already engaging schools, parents and business in a drive to improve the nation's literacy, daily maths and reading lessons in primary schools with support of the whole community, are needed.