Call Clegg marks the first time that a senior member of government has agreed to be challenged by listeners every week about "the big decisions being made in Downing Street".
Every Thursday at 9am, the deputy prime minister will go "head-to-head" with LBC 97.3 breakfast host Nick Ferrari in the half-hour programme.
Listeners will be able to call, email or tweet in their questions for Clegg. The first show will go ahead on January 10 at 9am.
Discussing the move, Clegg said: "I'm doing this because I don't think politicians get to hear enough from people directly. You can't do the right thing in government unless you keep in touch with how people are thinking and feeling."
He added: "Nick Ferrari is known as the interviewer that all politicians fear. He can be very tough but he's generally fair, very well informed and I hope we'll make a good combination for the show we're doing together."
Richard Park, the director of broadcasting at LBC-owner Global Radio, said that Call Clegg will be "London's biggest conversation".
He added: "No other station offers its listeners such unique access to a senior member of government. This will be must-listen radio."