Danes is best known for her work on TV's "My So-Called Life" and in the movies "William Shakespeare's Romeo & Juliet," "The Hours" and "The Family Stone."
Dancy has appeared on the big screen in "The Jane Austen Book Club," "Blood and Chocolate," "Savage Grace" and "Confessions of a Shopaholic."
The couple confirmed their engagement in February, People.com said.
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