Clegg, leader of the Europhile Liberal Democrats, will face Nigel Farage of the United Kingdom Independence Party (UKIP), which wants to pull Britain out of the European Union.
They will square up on London-based LBC radio on March 26, and again on BBC television on April 2.
There is no love lost between the pair. Clegg has said he will launch an all-out attack on the "myths" peddled by "isolationists".
Polls show right-wing UKIP has moved ahead of the centrist Lib Dems as Britain's third most-popular political party.
Also Read
"I wanted the British people to see that there is a very real choice at the upcoming European elections: between the Liberal Democrats as the party of 'in' and UKIP as the party of 'out'," Clegg said.
British Prime Minister David Cameron, the Conservative Party leader, wants to renegotiate London's relationship with Brussels and stage an in-or-out referendum by the end of 2017 if he remains prime minister after next year's general election.
"Europe is always a highly charged issue in British politics and this is a fantastic opportunity to test the arguments," said James Harding, director of BBC news and current affairs.
In Britain, the European Parliament elections will be held on May 22.
UKIP does not however have a single seat in the British parliament.