Out Among the Stars comes out in March and features 12 tracks by the American singer, recorded for Columbia Records in 1981 and 1984.
It includes duets with Cash's wife June Carter and friend Waylon Jennings.
The tracks have never been made public before.
They were not released at the time and the singer, who had fallen out of fashion, was later dropped by his record label.
The recordings came to light only when John Carter Cash found them, gathering dust in a vault, while he was cataloguing the singer's private archive in 2012. He found hundreds of reels of unreleased live and studio recordings in the vault, including duets with Bob Dylan.
It is the fourth posthumous album released since Johnny Cash died in 2003, aged 71.
Speaking to the BBC, Carter Cash said: "There is more music to be released that is unheard, there are some great recordings.
"But we don't want to release something unless it means something.
"It has to be in line with what we believe my father would have wanted released".
The unreleased recordings will bolster what is already a lucrative business for the Cash estate. In 2009, he sold more than three million records, reportedly earning more than $8m (Â£4.9m).
But Carter Cash maintained "the world would be a darker place" if the music was not released and it was "worth doing" if fans around the world wanted to hear it.
"Do you want to see another Picasso if there's one that nobody has ever seen before?" he asked. "I would say that probably the world would want to see another Picasso. And it's really the same thing. This is a work of art."
To date, Johnny Cash sold more than 90 million records. He is best known for songs including Ring of Fire and I Walk the Line and famously performed for inmates in American prisons.
"He would sing the songs for the underdogs," said Carter Cash. "He would reach out to people that no one else would reach out to."
Johnny Cash's son, John Carter Cash, has described a new album by his late father as "a great treasure",  saying there will be more records released in the future.