The two TV spots, shot in a documentary style, show the artists experimenting with one of their best-known tunes to give it a fresh perspective.
McCartney is seen reworking Wings' Band on the Run, while Stipe performs a new version of REM's biggest UK hit, The Great Beyond.
The films are set to break across the BBC network and will be supported by radio and poster activity. The posters will form part of a ten-day campaign incorporating 96- and 48-sheet posters focusing on the new presenter Jeremy Vine's weekday lunchtime show.
Nick Rowe, the marketing manager of BBC Radio Music Marketing, said: "BBC Radio 2's outstanding performance in recent years gives lie to the notion that music radio can only be popular if it slavishly follows formulaic formats. These films recognise that the British public is a very discerning market, which wants to be entertained and informed in a non-patronising way."
Radio 2 has enjoyed a growth in listeners in recent months. The latest set of Rajar figures showed its weekly reach was up to 13.3 million from 12.3 million, while its share of listeners was up from 15.2 per cent to 15.8 per cent. Its success has impacted on commercial rivals such as Virgin Radio.
The films were directed by the documentary director Kevin McDonald, written and art directed by John Cross and Andy Johns, and produced by BBC Broadcast.
Stipe added: "I like the idea of taking a song, breaking it down, and looking at it from a different perspective."
Meanwhile, the radio station is also maintaining its profile by broadcasting special programmes to British personnel in the Gulf.