The pair were friends since meeting at school aged 11
In a statement, McCartney emphasised the fun he and Aspinall had throughout their long association.
The former Beatle said: “I met him at school when we were both 11 and we remained friends ever since.
“I was able to say goodbye and thank him for everything he did for us and I send my deepest sympathies to his wonderful family.
“I will miss him but will remember the laughs, there were plenty.”
Aspinall, who died of lung cancer in New York City, was the head of The Beatles‘ Apple Corps until last year.