However the 1976 US Copyright Act means that he is set to claim the titles once more in five years.
"Paul's been fuming for decades. It's as much personal as business," a source told British newspaper The Sun. "Now he'll get back what's rightfully his."
Apparently tunes penned prior to 1978 turn into the property of the songwriter after 56 years.
The 71-year-old will soon start to collect royalties and licensing money each year.
He is expected to rake in funds for most of the band's famous hits by 2026.
McCartney's friendship with the late King of Pop diminished in 1985 when he was outbid in a Sony records deal.
Jackson, who collaborated with McCartney on Say Say Say in 1983, coughed up £31million for a chunk of the group's tunes.
McCartney recently admitted he sometimes has to remind himself to concentrate on stage.
He loves performing for his fans and still enjoys singing the iconic songs which made him famous. However, as they are so familiar to him he occasionally becomes aware that he isn't paying as much attention as he should be.
"It's scary, because sometimes I suddenly wake up in the middle of a show and think, 'Concentrate man! Come on, you've got an audience here!'," he laughed to Q magazine.
McCartney is often amazed by how talented he was at such a young age.
The cool lyrics make it more exciting for him to relive through his tracks.
"It's like time travel. Singing Eleanor Rigby and thinking, 'Keeping her face in a jar by the door,' that's a pretty cool turn of phrase," he admitted.