Rimes' publicist, Rhett Usry, confirmed Tuesday that the country singer and the actor "were engaged over the holidays and are very happy."
Both were married to other people when they fell in love with each other. Rimes, 28, and Cibrian, 37, co-starred in the 2009 Lifetime original TV movie "Northern Lights."
Cibrian's divorce from his wife of eight years was finalized in October. Rimes' husband filed for divorce a year ago. Irreconcilable differences was listed as the reason for both previous marriages ending.
