The former Beatles star, 83, met the 'The King', alongside his bandmates for the first and only time in 1965 when the group visited his home in Los Angeles in California.
Reminiscing about his Beatles days, McCartney raved about his experience meeting Presley and his wife Priscilla.
Appearing on BBC Radio 2's Tracks Of My Years, McCartney admitted the Beatles were already Elvis fans.
"He was really great. He was a very handsome guy - but we kind of knew that. We were fans," he said.
"We just followed everything he did, and we looked at any photo we could get. He wasn't a disappointment at all."
However, he admitted some memories of what happened that evening are "slightly skew-whiff".
"I say that we rang the doorbell and Elvis came to the door and said, 'come in guys'.
"He invited us in and we sat around and he had a jukebox, and played Mohair Sam, the record."
"Ringo says he didn't come to the door, we went in and he was sitting there. So who's right? I am," he joked.
McCartney described his time with the rocker as a "great evening".
"He played a bit of bass," he said.
"He had a bass there and he was talking about the bass so we could talk, sort of, bass talk. He was great, very personable, very nice.
"He had a bunch of his minders with him - and you read stuff later, and I think they were mainly his cousins, his gang."
He described meeting Priscilla a "highlight".
"You're inviting four guys into your home - probably the last thing you need is them to be all over your wife," he said.
"It was great, she was great, Elvis was great," he told host Vernon Kay.
"You pinch yourself. I met - I actually sat with, like I'm sitting with you, Elvis."
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