The debate is scheduled to go out on the BBC's Money Programme on 6 April, just as the general election campaign gains momentum. Malcolm Bruce, the Liberal Democrats' Treasury spokesman, will also appear.
Mr Brown's readiness to take on the Chancellor, who is a heavyweight speaker but quick on his feet, increases the pressure on John Major to stage a televised "battle of the Titans" with Labour leader, Tony Blair.
The Prime Minister has confirmed that discreet talks are under way in the possible form of a head-to-head TV confrontation. But he has not yet made up his mind whether to risk going ahead.
The Shadow Chancellor's "yes" to the contest coincides with a stinging personal attack by Mr Clarke, who told the Conservative Central Council two days ago: "Gordon, you can put on a Liverpool football shirt if you want to, but it won't make you Robbie Fowler. You can put on a miniskirt, but it won't make you a Spice Girl. You can put on suede shoes, but it won't make you a successful Chancellor."
Mr Brown's press secretary, Charles Whelan, said yesterday: "We hope the level of debate on the Money Programme will be higher than name-calling and speculation about what shoes Gordon will wear when he becomes Chancellor."
A senior aide to the Chancellor said Mr Clarke had accepted the invitation "in principle", subject to talks with the BBC about the format of the programme.
Mr Brown's style is not considered as agile as the Chancellor's, but he, too, is an experienced debater - dating back to his teenage years as a member of Kirckaldy High School debating society and a student politician at Edinburgh. It promises to be a formidable clash.
The Liberal Democrats have to be on the programme because of legislation on fairness in the media during general elections, but the real sparks will fly between Labour and the Government.
At the 1992 general election, the Money Programme tried to stage a similar debate between the late John Smith, the Shadow Chancellor and Chancellor Norman Lamont. The Conservatives pulled out at the last minute on the pretext that "a trade un-ionist" was on the experts' panel.
n Whoever is selected as Labour candidate for Newport East today is set for a job for life.
The winner will inherit a majority of almost 10,000 from the veteran Roy Hughes who is stepping down after 31 years as an MP.
His announcement last month sparked speculation that the Labour leadership to would try to shoe-horn in Alan Howarth who abandoned the Tories for Labour in 1995.
The MP for Stratford on Avon is one of four who will battle it out at the South Wales town's Ringland Labour Club.
The other hopefuls are Bryan Davies, whose Oldham Central and Royton seat is vanishing because of boundary changes, Reg Kelly, a Newport councillor, and Helen Jones, a solicitor and member of Labour's North Wales regional executive.