Harding, 67, known for his own music career including unlikely chart hit The Rochdale Cowboy before joining the station, hosts a weekly show and fronts the annual folk awards.
He will be replaced by presenter Mark Radcliffe on the show, which is broadcast at 7pm each Wednesday.
Harding said today that he was "not leaving the show of my own volition".
He added that he would continue to "present the music I love" until December 26.
Radio 2 controller Bob Shennan said: "I'd like to thank Mike Harding, who has spent 15 years at the top of his game, delighting fans with his expertise and rooting out the very best folk music.
"On his watch, folk has enjoyed a huge surge in popularity and Mike has been key in supporting the genre and introducing Radio 2 listeners to a broad range of new artists. We very much hope to work with him again in the future."
Radcliffe said: "I can't say how thrilled and honoured I am to be doing this. Anyone who knows me, or has seen one of my gigs, knows how steeped in folk I am and it is a joy to be able to combine work and pleasure like this.
"I am also well aware of how loved and cherished Mike Harding is and it is daunting to be following in his footsteps. He is a friend and someone I respect enormously and I really want to pay tribute to the sterling job he's done on the Folk Show for so long. Thanks Mike, from all of us."
Radcliffe already fronts his Music Club on Tuesday nights and hosts a weekday afternoon show with Stuart Maconie on Radio 6 Music.
Harding started gigging as a folk singer in the 1960s, later incorporating stand-up into his act. He fronted his own BBC TV series and has written several books, as well as writing music for TV shows such as cartoon hits DangerMouse and Count Duckula.