Murray, 31, took to Instagram to share a snapshot of an adorable gray baby onesie with a white elephant on it, along with a series of sonograms from McCaffrey's ultrasound.
"Baby Murray - 14th of January 2021," Murray captioned the cute pic, revealing his girlfriend's expected due date.
After being inundated with congratulations and well-wishes, Murray responded in the comments to his post, sharing, "We're both so happy, excited and nervous and can not wait until he/she are in our arms."
A rep for Grint and Groome told ET in May that the couple were "delighted to confirm the birth of their baby girl."
Speaking with Andy Cohen on an episode of Watch What Happens Live shortly after Grint became a dad, Harry Potter star Daniel Radcliffe said he was "so happy" for his friend, but that it also represented an unexpected milestone for Radcliffe.
"It's also super weird for me to think that we are all of the age where we're having children," he admitted. "But we definitely are and it's really cool."
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