The snapshot shows Green, 47, and Burgess standing on a balcony overlooking palm trees and an ocean shore.
The Beverly Hills, 90210 star holds Burgess' face as they share a kiss.
Green and Burgess recently went to Hawaii together, where the actor said they "had a really good time."
I feel blessed right now," he told Access Daily , explaining that he first met Burgess through their mutual business manager.
When asked by fans on Instagram over the weekend about her relationship status with Green, Burgess told her followers to " let it go ."
Last month, a source told PEOPLE that Green — who filed a petition for divorce from estranged wife Megan Fox in November — had "been seeing Sharna for a few weeks."
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