The song was broadcast simultaneously on Tuesday on BBC One, Two, Three, Four and Radio 1, 2, 4, 6 and 5 Live.
The track, which will also be released in aid of Children in Need, features 27 artists across all musical genres.
They include Sir Elton John, Stevie Wonder, Chris Martin, Sam Smith, Brian May, Jamie Cullum and Nicola Benedetti.
BBC local and national radio stations, BBC World Service, 1Xtra, 4 Xtra, Asian Network and BBC iPlayer and iPlayer Radio also came together to play the song at 20:00 BST (19:00 GMT).
BBC Radio 3, the BBC News Channel and BBC World News were due to air it shortly afterwards.
BBC Music will encompass TV and radio programming, digital services and schemes to support emerging talent including the introduction of classical music to UK primary schools.
The song's original writer, Brian Wilson, also features on the track, along with the BBC Concert Orchestra.
The collective group of musicians has been named the Impossible Orchestra.
Bob Shennan, director of BBC Music, said: "This 'impossible' orchestra is a celebration of all the talent, diversity and musical passion found every single day throughout the BBC."
The BBC's new music strategy was unveiled by the corporation in June.
Stars including Pharrell Williams and One Direction have recorded the Beach Boys track God Only Knows to launch the BBC's new music initiative BBC Music.