The song will be included in the upcoming film Last Christmas, starring Emilia Clarke and Emma Thompson, which is inspired by the singer's music.
Presenter Zoe Ball said: "I was, and am, a huge Wham! and George Michael fan and even though he is no longer with us, his music remains a joy to us all. I’m honoured to be premiering this previously unheard song from George on my Breakfast Show."
Jeff Smith, head of music at Radio 2 and 6 Music, added: "Ever since they burst into the pop charts in 1982 with Young Guns, the music of both Wham! and George Michael has been loved by Radio 2 listeners, so I’m thrilled that they will be the first to hear this very special record."
The star died on Christmas Day 2016 at the age of 53, with a coroner determining his death was due to natural causes.
Prior to his passing, Michael gave producer and writer Emma Thompson his blessing for the project which also stars Crazy Rich Asians actor Henry Golding.
The soundtrack to the film will feature three Wham! songs, including the titular Last Christmas along with 12 of Michael's solo tracks.
Director Paul Feig has said he was encouraged to expand the film's soundtrack from just one track when he began to explore the icon's back catalogue.
He told Yahoo Movies: “It started snowballing in prep. I was suddenly adding songs into the actual film that we would have the characters sing - but not in a musical way - just in a very organic way.
“And then once we got into post [production], then I started going, ‘Oh, this song actually can work really well in this scene.’ And so it just really built organically.
“It's not a jukebox movie, but it's not a musical either. I call it ‘a soundtrack to your life’ movie. We've all got songs that means so much to us, and this character in the movie [Kate, Emilia Clarke], she wants to be a singer and her favourite singer is George Michael.
“It’s this idea that one artist represents you and stays with you, as you're going through crises and going through the harder parts of your life.”