The pair will front shows for the station during the festive period as part of its aim of producing more comedy programmes.
Former rapper-turned comedian Brown will include a mixture of hip-hop and stand-up in a show titled Dong Comedy.
Comedians Marlon Davis, Michelle De Swarte and Fergus Craig will also appear in the show alongside beatboxer Hobbit and DJ Big Ted.
Nick Helm will host a Christmas variety show. It will feature "a festive helter skelter of jokes, singalongs, party games, new music, poems, and some of the finest young comedians on the circuit", the BBC said in a statement.
Both shows will be taped in front of a live studio audience, with broadcast dates still be confirmed.
Tom Deacon was recently announced to be hosting a new Wednesday evening comedy show on BBC Radio 1 in 2013.
Helm has also signed up to produce a Channel 4 comedy pilot named Uncle.
Watch Doc Brown on Russell Howard's Good News below: