The Beatles legend collaborated with his former bandmate on his 1997 solo album after the Electric Light Orchestra musician - who performed on and produced the record after previously contributing to 'Beatles Anthology' - suggested he got in touch.
As quoted by The Sun newspaper, Paul said: "I'd been saying to Ringo for years it'd be great to do something.
"We'd never really done that much outside The Beatles. One night, Jeff suggested, 'Why don't you get Ringo in?' and I said, 'OK!' "
The duo were "very comfortable" making music together again, with the three of them jamming together on what would become 'Really Love You'.
Reflecting now on what the drummer added to the record - which was reissued on July 31 with double CD and LP box sets as part of the 'Paul McCartney Archive Collection - Macca simply said: "Magic."
'Flaming Pie' track 'Little Willow' was an emotional one to record, as it was written about the tragic death of Ringo's first wife Maureen Starkey, who sadly lost her life to leukaemia aged 48.
Paul explained: "Even if I'm writing something very specific, I veil it. If I want to write about loneliness, it will be Eleanor Rigby who carries the can.
"With 'Little Willow', I was very affected by Maureen's death. The fragility of life is in that song. But it wasn't called Maureen, if you get what I'm saying. It was called 'Little Willow.' "
Last year, Ringo and Paul performed together on stage in Los Angeles, and the latter admitted he found himself reflecting on their storied history together as they played Beatles rocker 'Helter Skelter'.
He added: "He's drumming away and I'm singing facing front. But when I wasn't on the mic, in the solo breaks, I really made a point of turning round and watching this guy drum.
"And, my God, I'm thinking of the memories across this ten-yard gap -- him on the drums and me on the bass, the lifetime that's going on here. It is magic. These days, he and I get quite emotional about it, because we should."