The newlyweds are planning to celebrate with a family party at their New York home on May 6.
"I have found the quiet and happy life that I have always sought," the Pretty Woman actor told the magazine.
Gere, 68, and Silva, 35, have been dating for three years.
Silva previously told the magazine that "I was a little lost, without light, and knowing him gave meaning to my life. It was feeling that someone was reaching out and showing me my true path."
Silva told the publication that the couple are planning to start a family in the future.
The nuptials mark the third marriage for Gere, who was married to supermodel Cindy Crawford from 1991 to 1995 and model Carey Lowell from 2002 to 2016. He shares son Homer, 17, with Lowell.
It will be the second marriage for Silva, who was in the midst of her divorce from Govind Friedland, the son of mining billionaire Robert Freidland, when she met Gere. She shares son Albert, 5, with Friedland.
Marriage rumors spread earlier this month after the Daily Mail reported that Gere and Silva, a publicist and activist, planned to marry — and Silva was first spotted wearing a large engagement ring back in December.
"I am recently divorced. As far as a legal wedding, no, but maybe we'll have a celebration," Silva said during a red carpet interview back in June when asked if she'd ever marry again. "You know, the perfect couple is made of two people who can be what the other needs. I'm living the type of life you see in the movies, truly."
Gere has been an outspoken social activist in recent years, particularly over China's occupation of Tibet. He previously stated in an interview with The Hollywood Reporter that his political stance has hurt his ability to take on certain movie roles in recent years.
"There are definitely movies that I can't be in because the Chinese will say, 'Not with him,'" Gere said. "I recently had an episode where someone said they could not finance a film with me because it would upset the Chinese."0comments
"I'm still making the same films that I was making when I started," he continued. "Small, interesting, character driven and narrative driven stories. It hasn't impacted my life at all."
Gere's film career started off in 1975 when he played a role in the film Report to the Commissioner. He's since gone on to star in numerous critically acclaimed films such as An Officer and a Gentleman, The Cotton Club, Pretty Woman, Runaway Bride, Chicago, Primal Fear and I'm Not There.