The former X Factor judge, 68, shared a photo of the pair on their wedding day on 4 July 1982 in Maui, Hawaii where they tied the knot.
She wrote on Instagram: "Thank you for 39 years. For the most incredible life together. The crazy, wonderful and insane times. Yes, pain and sorrow too, but we got through it.
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"We worked so hard for years professionally and personally. We succeed together. You are my soul, my life. What a fantastic life we have lived so far, the best thing is there’s more to come.
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"Every day is an adventure, every day I love you more and respect you more. My soulmate, my love and my friend here’s to our next adventure! Love you always ~ Sharon."
In his own tribute, Ozzy, 72, posted another photo from the day of him placing a ring on his wife's finger during the ceremony. The Black Sabbath rocker wrote: "Happy Anniversary My Love! - July 4, 1982."
They welcomed their three children, daughters Aimee, 37, and Kelly, 36, and son Jack, 35, in the first four years of their marriage.
Ozzy has previously divulged that Sharon purposefully picked their wedding date, which is Independence Day in the United States, so he would remember it.
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They briefly split in 2016 following news that Ozzy had been unfaithful, reportedly with his hairstylist, Michelle Pugh.
He has since expressed his regret at his behaviour, telling GQ last year: "I got my reality check and I'm lucky she didn’t leave me. I'm not proud of that. I was pissed off with myself. But I broke her heart."