"We thrive playing for our country, representing the green and gold. There is always a lot of passion and pride and it is a great time of the year. We are in the Aussie summer, ready to start 2023. There is no better place to be," said De Minaur.
The inaugural United Cup brings together the best ATP Tour and Hologic WTA Tour players in an 18-country teams' event played over 11 days across three Australian cities - Brisbane, Perth and Sydney.
The pair had another reason to rejoice at the end of the year after an exceptional season in which they won the Australian Open doubles title and made their debut at the Nitto ATP Finals.
The top 16 nations' entries have been revealed, with Team Greece, comprised of world No 3 Stefanos Tsitsipas and world No 6 Maria Sakkari, being seeded first.
The Australian passed the stiff test against the Russian 7-6(11), 3-6, 6-3, 6-2, playing his aggressive game to triumph after two hours and 53 minutes.
The Russian will keep his World Number 1 ranking on the line against Kyrgios, who had defeated Medvedev at ATP Masters 1000 event in Canada to extend his head-to-head lead against him to 3-1. If he falls to Kyrgios, he will lose his World Number one crown.
The top seed was in command from the beginning of the match which lasted for two hours and 11 minutes. Medvedev started the match with a service break establishing his authority over the French player.
On the other hand, Hubert Hurkacz ended Nick Kyrgios' winning streak at the tournament as he clinched the match to enter the semi-final on Friday in Montreal.