"Rest In Peace George," he captioned the sentimental shot. "I'm heartbroken we never got to speak again after so many years, I can't believe this has happened, please watch over me in heaven Godfather. Enjoy paradise I love you. ❤."
Michael, who died of heart failure in his sleep at his country home in London, England, on Sunday, grew up with Kennedy's father, Andros Georgiou. The two were best friends -- they grew up together in Cyprus, Greece -- until a falling out in the late 1990s, after which Kennedy saw much less of his godfather.
On Sunday, Kennedy also shared a pic of his father with "Yog," Michael's nickname.
"Dad and Yog... 'God takes angels when he needs them'. Thank you all for your messages, bless you all. Dad, I'll be with you soon and can't wait I love you," he wrote alongside the black-and-white shot.
Kennedy tried to repair his relationship with the singer -- who is also godfather to his brother, Harry, among other children of his celebrity friends -- in June 2015, wishing him a happy birthday on Twitter.
"Happy Birthday Uncle @GeorgeMichael I know it's been a long time, you're in my prayers. See u soon one day I hope," he wrote.
Kennedy isn't the only one to pay his respects to Michael. Stars like Elton John, James Corden, Ricky Gervais and more remembered the GRAMMY winner with kind messages and sweet anecdotes on social media.