"And I said, 'Well, of course. How does this work?' And she said, 'Well, at about midnight I'll come and get you and then I'll lead you over to her and then you ask her to dance.'"
The Pulp Fiction actor said his heart was racing before he approached the princess.
"She looked up and me and I said, 'Would you care to dance with me?' and she said, 'Yes,'" he said. "I took her and the whole room cleared. We danced for what felt like 15 minutes," he recalled.
Diana and Charles were on their first joint visit to the US together. She had given birth to their second child, Prince Harry, a year earlier.
For Travolta, it was a "storybook moment" he would never forget.
"We bowed when it was over and she was off, and I was off, and my carriage turned into a pumpkin."
In previous interviews, he also described the "magical" time he spent dancing with the princess.
"There we were, dancing together like in a fairy tale. Who could imagine that something like this is going to happen to you one day? I was smart enough to register it in my memory as a very special, magical moment."