The Swedish DJ - whose real name was Tim Bergling - was found dead in Oman in April last year, aged 28.
Now a 16-track album of new material entitled Tim, which "he was close to completing", will follow on 6 June.
Proceeds from the LP will go to Tim Bergling Foundation, set up after his death to help prevent mental illness and suicide.
"When Tim Bergling passed away on April 20, 2018," a family statement read, "he was close to completing a new album.
"He left behind a collection of nearly finished songs, along with notes, email conversations and text messages about the music.
"The songwriters that Tim was collaborating with on this album have continued the process to get as close to his vision as possible."
Adding: "Since Tim's passing, the family decided not to keep the music locked away - instead they wanted to share it with his fans all around the world."
The statement arrived with a moving video, featuring Avicii in the studio and tributes from his family, and you can watch it above.
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