The actress is currently pregnant with her third child, the couple's representative has confirmed to People Magazine.
The pair, who wed in 2009, are already parents to two boys, sons Cyrus Michael Christopher, ten, and his little brother Rowan, who is four years old.
WATCH: The Cutest Celebrity Baby Photos
Claire and Hugh have had a pretty private relationship since the beginning of their romance, having met while filming the movie Evening in Newport, Rhode Island back in 2006.
Meryl Streep's daughter, fellow actress Mamie Gummer, who was also part of the film drama's cast, previously told People that their courtship had always been "low-key," telling them: "I was there when it was happening and it's something that I will never forget," adding: "I'm incredibly happy for them. They are perfect for each other."
Looking back on the start of her relationship and what sold her on the actor, the Fleishman is in Trouble actress, for which she was recently nominated for a Golden Globe, told Porter Magazine: "When we first started sorta-kinda-dating for real (ish), I had an ornament-making party for Christmas, and he helped organize it," and: "Then he made an ornament of cowboy paper dolls, and I thought, 'and he crafts?' That was it. You have me for the rest of our lives."
The couple met on the set of Evening
The pair got engaged in February of 2009, going on to tie the knot the very same year in September.
They held a private ceremony in France, and People reports that Claire donned a custom Narciso Rodríguez design as her wedding dress.
The two recently stepped out for the premiere of Claire's new hit series
Their most recent red carpet appearance was in support of Claire, with the two attending the Fleishman is in Trouble series premiere in New York City on 7 November.
Congratulations to the couple and their growing family!
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