According to The Guardian, the programme will be based on Llewellyn's web series Carpool.
The format sees the Red Dwarf star interviewing people while driving them around in his car. Previous guests have included Ruby Wax, Stephen Fry, David Baddiel, Jonathan Ross, David Mitchell and Patrick Stewart.
Dave has now ordered ten 30-minute episodes and has described the programme as television's "most intimate and off-the-wall chatshow".
Meanwhile, Llewellyn said: "I started Carpool 18 months ago as an experiment. A sort of talkshow recorded in a car as I drive busy people to meetings, events, gigs or just down the shop. The real joy is that people talk openly and intimately and it's not only funny but a real insight into the interviewees."
The online version of Carpool has been downloaded more than two million times on iTunes.