"Fun, adventurous, passionate, determined, honest, devoted, amazing father and the best head of hair in Los Angeles!" Kate wrote. "Lucky us! Love you Pa! Happy Fathers Day."
Kurt does not have an official Instagram account, but Goldie responded, writing, "Honey I showed this to daddy. Here's his message…"
The actor's comment was: "Birdie, mommy just showed me this picture, this perfect Father's Day present. I've never seen it before. Wow…it's a killer. Lotta water under the bridge…it's kinda hard to see it though cause all that water seems to somehow have found its way into my eyes…thanks for making me the luckiest father in the world sweetheart. I love you, Pa."
Drew Barrymore wrote, "@katehudson wow this one almost hurts its so sweet."
Goldie also commented that the photo "speaks volumes." She also shared her own Father's Day tribute to Kurt.
Kurt, 71, helped raise both Kate, 43, and her brother Oliver Hudson, 45. Goldie, 76, divorced their father, musician Bill Hudson, when they were little. She and Kurt also share son Wyatt Russell, 35.
Kate has occasionally paid tribute to "Pa" Kurt online.
"This is a man who made his family his number one priority his whole life," she wrote on his birthday in 2015. "Never missed a school play, a soccer game, a hockey game, a dance recital and the list goes on and on. No matter what he was doing in his busy life, he always showed up. Not because he had to but because there was no other place on earth he would rather be then with his family. We felt the purity of that our whole childhood and my gratitude for his love is immeasurable."
Also on Father's Day, Kate also paid tribute to her partner, Danny Fujikawa, with a video of him with their daughter Rani, 3, the youngest of her three kids. She also shared posts dedicated to her brothers, who are also dads.
See more celebs' Father's Day tributes below: