"Yes, they were engaged over the holidays and are very happy," her rep tells PEOPLE exclusively.
A source adds that the couple, who spent Christmas at home in Los Angeles, "had family and close friends in town who helped them celebrate."
Rimes, 28, and Cibrian, 37, were spotted on a Malibu beach on Monday, where she was wearing a new engagement ring.
The platinum sparkler features a 5-carat oval diamond set in rose gold fleur-de-lis connected to the band, according to a source.
"The couple wanted an antique feel, but a new ring," says the source, who adds that Rimes and Cibrian designed the ring together with the actor's childhood friend Brent Polacheck at Polacheck Jewelers.
On Monday afternoon, Rimes thanked fans for their support, writing on Twitter, "Thank you for all your well wishes!! We are extremely excited and look forward to a beautiful future. It's been an incredible last few days, I was shocked!!! We are blessed, our families are so happy and our lives are filled with love."
Road to EngagementIn November, engagement rumors kicked into high gear after the couple posted a photo on Twitter which showed Cibrian on bended knee holding Rimes's hand. Later that month, Rimes slammed new reports of an impending wedding as "150 percent untrue."
Rimes and Cibrian met while filming the Lifetime original movie Northern Lights at a time when they were both married to other people. The singer has talked openly about the difficulty of falling in love with Cibrian and ending her marriage to Dean Sheremet.
"We make mistakes and we learn from them, but we're human. We fell in love," she said in November of Cibrian. "We're really happy in what we feel privately."
The singer's divorce from Sheremet was finalized in June. Sheremet himself got engaged in November and Rimes congratulated him in a Tweet, wishing him "a life full of happiness."
When she marries, Rimes will officially become stepmother to Cibrian's two children, Mason, 7, and Jake, 3. (Cibrian shares custody with his ex, model Brandi Glanville.)