The tournament - which has replaced the short-lived ATP Cup men's team event as the 2023 season opener and concludes on January 8th with the final - features 18 countries with ties played in Brisbane, Perth and Sydney.
Each tie features two ATP and two WTA singles matches and one mixed doubles match, which could decide the winner if teams are locked at 2-2.
"I have to say it's great. I'm very happy with this idea that they came out with. I was always jealous of the (men-only) Laver Cup and the ATP Cup. Finally we're in as well," twice Grand Slam champion Kvitova told reporters.
The mixed-gender Hopman Cup team tournament was axed in 2019 much to the displeasure of fans, many of whom celebrated news of its return this year.
The next edition will be played in France in July, boosting the presence of popular mixed team events on the global circuit along with the United Cup.
Kvitova, who sealed two straight wins in the United Cup, said it was a pleasure to be part of the event.
"I really enjoyed every day. Long days, for sure... I couldn't celebrate New Year today. It's tough. Otherwise it was fun, especially with the boys," Kvitova said, referring to the younger male players on the Czech team.
"It's always different. They're young. They have a different energy. It's fun to be in a team with Marie Bouzkova as well and Jesika Maleckova. I've never been in a team with them. It was really fun."
Ruud, runner-up in last-year's French Open and U.S. Open, said he was delighted that young women players could share the platform with top names.
"They have players like Iga Swiatek here that they can look up to. Belinda Bencic is here as well," Ruud said after Norway fell 4-1 to Brazil in the United Cup on Sunday.
"The girls from Norway don't typically see these types of players at all during the year, so to see them up close is a good experience and hopefully, it's some motivation and inspiration to see them."
