"This is the most beautiful moment I could have ever hoped for. You've successfully made me the happiest, luckiest woman alive," she wrote.
"I can't wait to show you my unfaltering immeasurable love for the rest of our lives. #engaged #loveofmylife #futurehusband."
A couple hours after posting the video Greene shared a snap of her huge, oval-shaped sparkler with fans.
She captioned the photo: "I'm SO lucky and SO excited that I get to spend the rest of my life with my best friend but the ring doesn't hurt either. It's the most beautiful thing I've ever seen".
Her husband-to-be also shared the video with his own Instagram followers.
"I promise to put a smile on your face for the rest of our lives," the Aussie TV personality wrote in his post.
"You complete me in ways I didn't even know was possible. I love you more than anything and excited to take this next step in life with you! #foreverlove #myfutrewife #ShesGonnaBeAKhoury (sic)"
The pair have been together since 2013. But the relationship wasn't Greene's first high-profile romance. She previously dated Joe Jonas, formerly of the Jonas Brother, who is now in the band DNCE.