Garson died Tuesday at age 57 after suffering from pancreatic cancer. He was perhaps best known for his role as Stanford Blatch, the best friend of Sarah Jessica Parker's Carrie Bradshaw, in the popular HBO series and its spinoff movies.
On Wednesday, Davis, 56, shared a series of photos of Garson on her Instagram page, including one of him with his son Nathen. In the caption, she recalled the origins of her friendship with the actor.
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"I first met Willie in 1995 on the spooky nighttime set of the X-files," she began. "He immediately made me laugh. Little did I know that we would have the joy of sharing Sex and the City + And Just Like That together. Willie is beloved by our entire community. He was smarter and funnier than you ever would have imagined. We are bereft without him."
Davis, who plays Charlotte York in the beloved franchise, continued, "But I really want to pay tribute to his fearless commitment to single fatherhood. We spoke about being single parents through adoption often. And nothing gave him more joy and pride than his son Nathen. Nathen's strength and wisdom beyond his years are evident in his beautiful tribute to his dad. The outpouring of love is earned dear Willie."
"I am thankful for all of the time we had and grateful that so much of your bright light is on film forever," she concluded. "Maybe we can do our pod cast [sic] the next time around ? We love you forever xoxo."
Various other members of the SATC family also paid tribute to Garson following the news of his death, with creator Darren Star describing him to PEOPLE as "sweet, soulful and hilariously funny."
"Willie touched all of us with his big heart and generous spirit," Star said. "The man behind Stanford was a loving father, a mensch to his friends and radiated kindness to all. He is gone much too soon."
getty Willie Garson with Sex and the City costars Kristin Davis, Sarah Jessica Parker, Cynthia Nixon and Kim Cattrall
Nixon, who starred as Miranda Hobbes in the original series and is reprising her role for the reboot, shared her tribute on Twitter.
"So deeply, deeply sad we have lost @WillieGarson. We all loved him and adored working with him. He was endlessly funny on-screen and and in real life. He was a source of light, friendship and show business lore. He was a consummate professional— always."
Mario Cantone, Garson's on-screen husband in SATC, posted a photo of the friends on Instagram Tuesday, sharing his grief in the caption.
"I couldn't have had a more brilliant TV partner. I'm devastated and just overwhelmed with Sadness," Cantone wrote. "Taken away from all of us way soon. You were a gift from the gods sweet Willie. Rest …I love you."
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Executive producer Michael Patrick King, meanwhile, told PEOPLE that Garson's "spirit" and "dedication" were ever-present on set.
"The Sex And The City family has lost one of its own, our amazing Willie Garson," King said. "His spirit and his dedication to his craft was present every day filming And Just Like That... ."
"He was there — giving us his all — even while he was sick," King continued. "His multitude of gifts as an actor and person will be missed by everyone. In this sad, dark moment we are comforted by our memory of his joy and light."