Murphy said Pryor was aware of him and his work on Saturday Night Live, although Murphy was not yet a big star. He approached Pryor and gave him a copy of his first comedy album.
"I went over and I gave it. I said, 'Mr. Pryor, I'm Eddie. Will you listen to my--' He said, 'Oh yeah, I know who you are,'" Murphy recalled.
"He put the cassette in, put on the headphones," he said. "I was sitting behind him, watching him listening to my record. That was my first time meeting him."
Murphy said he could hear Pryor laughing at the album with his "weird laugh" a couple seats in front of him. After the plane landed, Pryor offered to give Murphy a ride.
"He had his driver [meet] him at the airport with his car. He said, 'Which way are you going?'" Murphy said. "He drove me to the house I was staying at. That's the way I met my idol, like that."
Murphy most recently starred in Coming 2 America, the sequel to his 1988 film Coming to America. The movie features Murphy's daughter Bella Murphy, 19.
On The Late Late Show, Murphy said working with his daughter on Coming 2 America was an amazing experience.
"Being on the set with my baby girl ... You know if you have children what it's like to see your kids do anything. But to have them come to work with you and actually be contributing and doing a great job, I was filled up every day just looking at her."
"You feel like your heart is going to burst," he added. "It's an amazing feeling."
Murphy has nine other children, many of whom are also interested in entertainment.
"A lot of my kids have interest in the arts and are acting and writing," he said.
Coming 2 America was released on Amazon Prime Video last week.