The song - which will get its worldwide premiere on Ken's show - is called 'Face It Alone' and includes Freddie's iconic vocals, taken from the 'Miracle' sessions in 1988.
Over the summer, Brian and Roger spoke to Zoe Ball on BBC Radio 2 as part of Queen Elizabeth's Platinum Jubilee celebrations, and they revealed they had discovered the song.
Roger said at the time: "Yes, we did find a little gem from Freddie, that we’d kind of forgotten about. And it was.
"It's wonderful. Actually, it was real discovery. It's from the 'Miracle Sessions', and I think it's going to be out in September."
His bandmate described the song as "beautiful" and touching", and explained how they ended up bringing it together.
Brian added: "It was kind of hiding in plain sight. We looked at it many times and thought, oh no, we can't really rescue that.
"But in fact, we went in there again and our wonderful engineering team went, okay, we can do this and this. It's like kind of stitching bits together."
Freddie died in November 1991, nine months after 'Innuendo' - their final album, and the successor to 'The Miracle' - was released.
In 1995, the band - including former bassist John Deacon - dropped 'Made In Heaven', the iconic lineup's final album as their frontman appeared posthumously on the collection.
Brian and Roger continued to perform live with singer Adam Lambert, and he joined them at the Platinum Party at the Palace concert over the summer when they had the honour of their song 'We Will Rock You' being tapped out by the Queen, who later died on September 8, during a skit she filmed with Paddington Bear.
Ken Bruce has the world exclusive first play of 'Face It Alone' on his Radio 2 show on Thursday, October 13 just after 11am.
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