The Beatles legend and the 'Superstition' hitmaker - who last worked together on 1982 song 'Ebony and Ivory', which was a number one hit in the UK and US - have teamed up to record 'Only Our Hearts', one of two original compositions included on his forthcoming record 'Kisses On The Bottom'.
Paul - who worked with Stevie at Los Angeles' Capitol Studio - said: ''Stevie came along to the studio in LA and he listened to the track for about ten minutes and he totally got it.
''He just went to the mic and within 20 minutes had nailed this dynamite solo. When you listen you just think, 'How do you come up with that?' But it's just because he is a genius, that's why.''
Paul's new album - which is set to be released on February 6 - teamed up with Eric Clapton on the record's other new composition, 'My Valentine'.
As well as the two new songs, 'Kisses On The Bottom' features a collection of standards that Paul first heard his father perform on piano at home during his childhood.