As head of music policy at Radio 1 between 1997 and 2000, Smith founded the Evening Session programme and recruited names including Chris Moyles, Steve Lamacq and Trevor Nelson.
He has also worked in programming roles at the BBC World Service and Capital Radio and in the mid 1990s worked in independent production at Wise Buddah as director of programmes.
Lesley Douglas, controller of Radio 2 and BBC 6 Music, said: "Colin Martin is a very hard act to follow but I have no doubt that Jeff's love of music, industry experience and recent role at Napster puts him in a unique position to move Radio 2 forward."