Roberts and Moder, a cinematographer, were married on a ranch in Taos, New Mexico on 4 July 2002.
The couple met on the set of 2001 film The Mexican, in which Roberts starred alongside Brad Pitt.
Roberts was dating fellow actor Benjamin Bratt at the time, while Moder was married to make-up artist Vera Steimberg.
After Moder’s divorce from Steimberg was finalised a year later, he and Roberts exchanged their vows, going on to have three children together.
The Pretty Woman star commemorated her and Moder’s wedding anniversary by sharing a picture of them together on Instagram, in which she is kissing her husband on the cheek.
“18 years #heckyes,” she captioned the photograph.
In late June, Roberts posted a tribute to Moder on Instagram for Father’s Day, sharing a picture of her spouse walking along the beach carrying a surfboard.
“Happy Father’s Day to all the fathers and father figures. Most especially this man. Our compass and unfaltering inspiration,” the 52-year-old wrote in the caption.
The couple’s twin daughter and son, Hazel and Phinnaeus, were born in November 2004, and their third child, Henry, was born in June 2007.
Roberts was previously married to singer Lyle Lovett from 1993 to 1995.
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