According to Burke's representative, the 39-year-old mother of four and 39-year-old Charvet reportedly exchanged vows in St. Barts on Friday.
Burke alluded to the fact she had wed the actor to her followers on Twitter Saturday morning but declined to formally announce the news.
"Morning tweeties. [I'm] waiting for LA to wake up... big news to share," she wrote.
Burke subsequently announced her marriage and then later apologized for keeping the couple's big day under wraps.
"Sending my 1st good morning tweet as Mrs. Charvet... Its true, we finally did it with love and certainty. OMG, I am a married woman!!!" the host tweeted on Sunday.
"Sorry to be so secretive, but we REALLY needed a private moment just for us for all the right reasons. Love you guys xoxo."
The newlyweds have two children together -- a three-year-old son named Shaya and a four-year-old daughter Rain -- while Burke is also a mom to her two daughters, nine-year-old Sierra and 11-year-old Neriah, whom she had from her previous marriage to Garth Fisher.