The actress took to Instagram on Thursday to share the sweet pic, which she captioned, "Mama Goldie and Pa killing it 80's style."
"Forgot to post a note on my parents 34th Anniversary so I figure why not now," Hudson continued. "A belated happy one my dear parents. Love you madly, deeply, profoundly. #HairGoals #Love."
Hawn and Russel began dating in 1983. While never officially married, the couple have been together for over three decades and welcomed a son, Wyatt, in 1986.
While Hudson is Hawn's daughter from her marriage to musician Bill Hudson, the Almost Famous actress is estranged from her biological father, and has long referred to Russell --whom she grew up with -- as her dad.
Despite both of their long careers in Hollywood, Hudson and Russell only recently acted together for the first time in last year's Deepwater Horizon. ET spoke with the actress about the experience, and what it was like learning from the veteran star.
"Growing up watching him work, he's such a pro and I think it was a great lesson for me when I was younger as to what kind of actress I wanted to be and the person on set I wanted to be," Hudson said. "I just love everything he's done." Check out the video below to hear more.