The Emmy Award-winning talk-show host arrived in Sydney with her mom, Betty DeGeneres, and de Rossi on Friday after a 14-hour flight from Los Angeles for a six-day filming trip to Australia.
"I'm moving here, it's so beautiful," DeGeneres told 3,000 admirers, who were clearly delighted to be in the sun-bathed Royal Botanic Gardens near the Sydney Opera House for the two-hour recording despite the 30-degree Celsius (86-degree Fahrenheit) early afternoon heat.
Guests included Oscar-winning actor and Sydney local Russell Crowe. He presented the 55-year-old host with two kangaroo-hide cattle whips that he said DeGeneres might need to catch "some brumbies" - an Australian term for wild horses - when she visits Australia's southeast. The pair took turns at whip cracking.
Asked by one emotional fan whether she and her wife would adopt her, DeGeneres replied, tongue-in-cheek: "We were just saying we should adopt someone. It's so easy for us."
The show was packed with games involving audience members, including an Australia-themed trivia event in which fans had to take a harbor plunge for a wrong answer.
"The Ellen DeGeneres Show" is in its 10th season. DeGeneres was honored with the Mark Twain Prize for American Humor last year.