The two, who present the 1pm-3pm afternoon show for BBC Radio 1, are two of the longest-serving DJs at the station and are former breakfast show hosts, taking over after Chris Evans left in 1997.
Lesley Douglas, the new controller of BBC Radio 2 and BBC 6 Music, has confirmed that Radcliffe will be joining Radio 2 later in the year and Marc Riley, aka Lard, will be joining BBC 6 Music in April.
"It's no secret that I've been talking to them for a long time. It makes perfect sense for them to move from Radio 1 to Radio 2 and 6 Music. I have been discussing this with Radio 1 controller Andy Parfitt for some months now and I am pleased that BBC Radio can provide a home for such exceptional presenters," Lesley said.
The change is one a number of the station that has seen it move away from rock to more urban music. The two will see their afternoon slot go to Colin Murray and Edith Bowman in the spring.
The Manchester-based pair have been on the station as a duo for more than 10 years and built up a cult following with their support for alternative music and their offbeat brand of humour.
A spokesman for the station said: "Mark and Lard have had a fantastic 10 years on Radio 1. We wish them well in their new homes."
With Mark and Lard gone, Jo Whiley is now the longest-standing daily presenter with 11 years at the station, although John Peel remains the longest-serving DJ at the station.
Radcliffe began his career as a radio producer and became a presenter on BBC Radio 5 when it launched in 1990. He came to Radio 1 in 1991 and was given a daily late-night show on which Riley, a former guitarist with Mark E Smith's band The Fall, was a regular guest.
The presenter and sidekick partnership won the two a cult audience taking them all the way to the flagship breakfast show to replace Evans. They were succeeded by Zoe Ball, who has herself long since left the station.
Over the years the pair have won three gold Sony Radio Awards between 1998-2001.
According to Riley: "We have been sat at opposite ends of the table shouting at each other for 10 years now and the plan has always been that once we were finished at Radio 1 we would go our separate ways. Luckily we stumbled across Radio 2 and 6 Music."
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