Australia will face Belgium in the Davis Cup semifinal in September.
Nick Kyrgios completed Australia's win over the USA on Sunday, with a straight sets victory over Sam Querry on Pat Rafter Arena.
Kyrgios' 7-6, 6-3, 6-4 win over Querry gave Australia an unassailable 3-1 lead following two wins in the singles on Friday, before losing the doubles rubber in five sets on Saturday.
Lleyton Hewitt's men will now face Belgium, after they defeated Italy 3-2 in Charlerol.
Australia last made the final in 2015, losing to Great Britain, who won the title.