For the first time, the host nation fielded two teams in the tournament, and Kyrgios and Gavrilova went through the week unbeaten. Australia Green, culminating in their 2-0 win over Ukraine gave Australia their second Hopman Cup title.
Both players won their singles matches in the final in straight sets, with the mixed doubles not being played. Nick Kyrgios secured the Hopman Cup for Australia Green by beating Alexandr Dolgopolov 6-3 6-4.
Kyrgios' team-mate Daria Gavrilova had earlier defeated Elina Svitolina 6-4 7-6 (8-6) in the mixed event. Svitolina had six set points at 6-1 in the second-set tie-break but lost the last seven points of the match.
Kyrgios, ranked 30th in the world, beat Britain's world number two Andy Murray in the group stage on Wednesday.
"It means a lot, it is my first real title to have won," Kyrgios said. "It is the perfect way to start the year, I haven't lost a match yet and I am riding a lot of confidence into the Australian summer.”
The pair were just one point from being eliminated from the tournament when they faced a match point against France in the deciding mixed doubles on Friday night, however they were in total control in the final.
"It is the biggest event I have ever won and just representing Australia for the first time and winning this title straight away is amazing," Gavrilova said. She was naturalised last month only.
Britain’s Andy Murray and Heather Watson thrashed Germany 3-0 on Friday, but saw their hopes of reaching the final dashed as Australia Green snatched top spot in Group B in Perth.