In an interview with Access Daily, published on Saturday, the Beverly Hills, 90210 actor, 47, said things are "going really well right now" — but that the pair aren't in a rush to put a label on their relationship.
"It's all going really well right now. It's early on so we don't have any labels for anything, obviously," he added, going on to praise the Dancing with the Stars pro. "She's an amazing woman. She's super responsible, she's super sweet and caring, passionate, fun to be around. I feel blessed right now."
As for how they first met, Green said they were introduced through their mutual business manager. "She was like, 'Hey I've got a client that you should meet,' " Green recalled, admitting that he "begrudgingly" agreed to meet with Burgess.
Of course, things changed after that first day. "We met and we had great conversation," the father of four added. "It's been great so far."
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Over the weekend, Burgess also declined to go into specifics when asked about her relationship status.
"Y'all don't give up on this one," she wrote while doing a social media Q&A with fans. "It's almost impossible to fish out real questions amidst ones about my relationship status. I say this with love and kindness. Let it go."
Burgess and Green were photographed last Saturday sharing a passionate embrace on the beach in Kona, Hawai.
Earlier that week, a source told PEOPLE that Green "has been seeing Sharna for a few weeks."
"They are casually dating and having a good time. They are currently vacationing together," the source said. "Brian was happy to leave L.A. for a few days."
He filed for divorce a day before Thanksgiving and requested joint legal and physical custody of the former couple's three sons — Journey, 4, Bodhi, 6, and Noah, 8 — in a court filing obtained by PEOPLE.