The victory was the first by a home pairing at Melbourne Park since Mark Woodforde and Todd Woodbridge — widely known as the Woodies — in 1997.
Kyrgios and Kokkinakis entered the tournament on a wild card and became heavy crowd favorites as they took out seeded teams from the second round to the semifinals.
They received the winners trophy from Woodforde and Woodbridge.
“I don’t know how we’re doing this, to be perfectly honest,” said Kyrgios, who lost in the second round of the singles draw to US Open champion Daniil Medvedev, who will face Rafael Nadal in the men’s singles final Sunday.
In another final Saturday, top-seeded Bruno Kuzuhara of the United States added the Australian Open junior singles title to his earlier doubles crown in incredible circumstances at Melbourne Park.
Kuzuhara beat fourth-seeded Jakub Mensik 7-6 (4), 6-7 (6), 7-5 in a match that lasted 3 hours, 43 minutes and ended with the Czech player having serious cramping that barely allowed him to continue serving.
Mensik fell to the court several times with cramps, finished with a pair of double-faults and had to be taken off Rod Laver Arena in a wheelchair.
The 17-year-old Kuzuhara has Japanese heritage, was born in Brazil and moved to the U.S. with his parents when he was an infant.
“First of all, it’s an unfortunate way to win it,” Kuzuhara said during the trophy presentation. “It was a great fight. We pushed each other right to the end.”
The Florida-based Kuzuhara won the junior boys doubles title with Coleman Wong of Hong Kong. They beat American Alex Michelsen and Adolfo Daniel Vallejo of Paraguay 6-3, 7-6 (3).