The introspective 14-track record, titled The Boys Of Dungeon Lane, recounts a collection of memories from the singer's formative years in Liverpool including his early adventures with his late bandmates George Harrison and John Lennon, prior to their Beatles fame.
McCartney named the album after Dungeon Lane, a place close to his childhood home in Forthlin Road in the Liverpool suburb of Speke.
It is referenced in the newly released track Days We Left Behind, which McCartney described as a "memory song" that inspired the album title.
McCartney said: "I was thinking just that, about the days I left behind and I do often wonder if I'm just writing about the past but then I think, how can you write about anything else?
"It's just a lot of memories of Liverpool.
"We didn't have much at all but it didn't matter because all the people were great and you didn't notice you didn't have much."
The record will also feature a number of new love songs and reflections from the artist on his life before he found global fame.
McCartney's new studio album was produced by Andrew Watt and began nearly five years ago with the opening track As You Lie There.
The Beatles was formed in 1960 and made up of McCartney, Lennon, Harrison and Ringo Starr.
The group became the best-selling musical act of all time and one of the most influential groups in the world, having achieved 16 UK number one albums and 18 UK number one singles including Help!, Hey Jude and She Loves You.
Following their split in 1970, McCartney released his debut solo album McCartney.
He also formed the band Wings with his late wife Linda McCartney along with former Moody Blues guitarist Denny Laine.
Prior to splitting in 1981, the band recorded seven studio albums including Band On The Run and achieved 12 UK top 10 singles including Jet, Silly Love Songs and Live And Let Die, the theme to the 1973 James Bond film.
McCartney's new album The Boys Of Dungeon Lane will be out on May 29.
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