The "Dallas Buyers Club" star was taken aback when he first met the 34-year-old model but insists he wasn't looking for a relationship at the time, reported People magazine.
Recalling his first meeting with the brunette beauty, McConaughey said, "I was very happily single and healthily single. I was not looking. I was sleeping well, I was spiritually sound, I was good hanging with me.
"Out of the corner of my eye, this sort of aqua-green figure went floating across the frame about 20 feet in front of me. My eye went up and I remember what came out of my mouth, 'This is not the kind of woman you call over across the room, McConaughey. Get off your chair and go get her', Which I did", he added.
"The self-respect she had, the way I understood her and her relationship with family, the way she respected me but never took anything for granted, not putting on any airs whatsoever," the 46-year-old star revealed.
The couple have three kids, Levi, Vida, Livingston.
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