The audition discs will be released by Decca, with What A Difference A Day Makes released as a single on Friday to mark the 80th anniversary of VJ Day.
Further previously unheard and rare tracks from them will feature on a new album called Hidden Treasures, which will be released on 7 November.
Dame Vera made her name during the Second World War, when her rousing songs such as We’ll Meet Again, (There’ll Be Bluebirds Over) The White Cliffs Of Dover and There’ll Always Be An England, earned her the affectionate name Forces’ Sweetheart.
Her final studio album, Unforgettable, was released in 2010.
She died in June 2020, aged 103, after she became the oldest artist to have a top 40 album in the UK, in May that year, with her greatest hits album 100.