The actor fell in love with the Welsh star after meeting her at a film festival but Zeta-Jones insisted on taking things slow.
Douglas then called on basketball legend Riley - the sports coach who inspired his iconic Wall Street character Gordon Gekko - to vacation with him and help him win over the girl of his dreams.
The former Los Angeles Lakers leader tells Men's Journal magazine, "My wife and I are sitting in our backyard doing nothing, and we get a call from Michael. He says, 'Why don't you come over to Majorca?'
"We fly over and we're coming into the harbour, and we see two people sitting on the dock with a bottle of champagne. It's Michael and Catherine. I said to him, 'Why the hell did you want us to come over? You're here alone with a beautiful woman.'
"He smiled and said, 'I wanted her to see me with a normal couple.'"
Douglas and Zeta-Jones married in November, 2000 and are about to celebrate their 10th year as husband and wife.