Sheremet found out about the affair when surveillance video footage of the couple kissing in a restaurant was leaked to the media.
He's since found love with photographer Sarah Silver, and Rimes showed she's still on friendly terms with her ex by 'tweeting' a message of congratulations after discovering Sheremet had proposed to the snapper.
In a post on the microblogging site, she writes, "Congrats to Dean Sheremet and Sarah Silver on your engagement! A little birdie told me the happy news last night. Wishes for a life full of happiness."
Rimes and Sheremet's divorce was finalised in June (10).
The dancer's engagement news comes shortly after Rimes was forced to deny rumours she is planning to wed Cibrian.