"Meghan sent me a playlist with some bare tunes on it," the star said.
When asked to disclose what songs made the set, Elba, 46, shared: "There was some West Coast on it."
"I'm not gonna put their business out like that, that's not fair," Elba said during the interview. "Ask Meghan and Harry."
Meghan, 37, and Harry, 34, said "I do" in front of about 600 guests at St. George's Chapel in Windsor Castle.
The couple celebrated their one-year wedding anniversary in May by releasing a charming set of-behind-the-scenes pictures on their joint Instagram account.
The slide show begins with a gorgeous black-and-white photo of Meghan and Harry from inside Windsor Castle's St. George's Chapel, and also shows the blushing bride holding the hand of her mother Doria Ragland and signing the wedding register alongside the Archbishop of Canterbury, who married them.
Another stunning shot showcases Meghan taking a bouquet from one of her bridal party and receiving some last-minute checks to the veil over her Givenchy dress.
As Meghan and Harry continue to celebrate their love, Elba is celebrating a union of his own.
The two exchanged vows on Friday at the Ksar Char Bagh hotel in Marrakesh, according to British Vogue. The Ksar Char Bagh is a small luxury hotel with extensive gardens in the palm grove of Marrakesh.
"It was one of the most beautiful three days of our lives. We spent a while trying to prep this wedding and wanted to have our entire family connection," Elba said on BBC Radio 1Xtra.
"We both have a big family and network of friends. We brought everyone together, flew to Morocco and had an amazing time," he added.