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Pearl Jam's Eddie Vedder and Jack Johnson will also appear on the record. The CD will be released on Johnson's record label later this year.
It will be accompanied by a DVD, which includes a video for Drake's 'Black Eyed Dog' filmed by late actor Heath Ledger.
"No-one in the world has ever seen that before," David Schulhof of Evergreen Copyrights told the BBC.
Drake, who released the albums Five Leaves Left, Bryter Layter and Pink Moon, died in 1974 aged 26. He is regarded as one of the most influential folk songwriters of all time.
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