Chmerkovskiy proposed to Smirnoff while the couple was spending New Year's Eve at the Wynn Hotel in Las Vegas, People magazine reported Sunday.
"They are really cute together," a source told People.
Representatives for the couple declined to comment on the engagement.
Chmerkovskiy joined Dancing with the Stars for its second season, while Smirnoff first participated in the show's third season. The couple reportedly began dating about six months ago, following Smirnoff's breakup with Mario Lopez -- her third-season dancing partner on the show.
Chmerkovskiy and Smirnoff both competed in the seventh season of the show that aired this fall. Chmerkovskiy competed with two-time Olympic gold medalist beach volleyball player Misty May-Treanor while Smirnoff competed with celebrity chef and former The Restaurant star Rocco DiSpirito. Both are currently participating in the show's winter tour.