But now it's being reported that the Hollywood star and the Joe Le Taxi singer are on the brink of splitting after constant rows.
A source told RadarOnline: "People around him are worried about how Johnny is doing because he and Vanessa seem so fractured right now."
The celebrity website says the 48-year-old Rum Diaries actor has "started reaching out to lawyers, probably to quietly discuss how to get out of the relationship".
Stories about trouble in the couple's relationship surfaced in the French press in April when Voici magazine published a picture that appeared to show him kissing another woman.
She was identified as his publicist Robin Baum.
Johnny has been with Vanessa, 39, since 1998, and though they never married they have two children – Lily-Rose, 12, and Jack, nine.
The attraction was instant, he said, when he saw the French beauty on the set of the Ninth Gate.
"She was wearing a dress with an exposed back and I saw that back and that neck, and then she turned around and I saw those eyes, and – boom! – my life as a single man was done," he said in an interview last year.
"You have this feeling," he added. "I can't really explain what it was, but I had it when I met her.
"I saw her across a room and thought: 'What's happening to me?'."
The family split their time between homes in Meudon in the Paris suburbs, Los Angeles, the south of France and a private island in the Bahamas.
Before getting together with the French actress Johnny had high-profile relationships with Kate Moss and Winona Ryder.
He was married briefly in the Eighties to makeup artist Lori Anne Allison.