"Happy birthday @bradfalchuk you are the grounding force, the epitome of love and kindness. Thank you for being my beacon," Paltrow captioned the post.
Paltrow confirmed her engagement to Falchuk in an issue of Goop magazine in January after more than three years of dating.
She said in a statement at the time that she feels "incredibly lucky" to have found the producer.
"We feel incredibly lucky to have come together at this juncture in our lives when our collective successes and failures can serve as building blocks for a healthy and happy relationship," the star said.
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Paltrow and Falchuk looked the happy couple while celebrating Valentine's Day together the next month.
"V-Day dinner last night," Falchuk captioned a photo of himself and Paltrow sharing a kiss. "Thanks @jessseinfeld for the recipies. #foodswings."
Paltrow was previously married to Coldplay singer Chris Martin, from whom she split in 2014 after 10 years of marriage.
She shares 13-year-old daughter Apple and 11-year-old son Moses with the recording artist.
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