The Jamaican currently holds world records in the 100m, 200m and 4x100m with times of 9.58s, 19.19s and 36.84s respectively
There were fears that Finch might not recover from a side strain he has been nursing for a fortnight, but the batsman was given the all-clear to open the innings with David Warner.
"I was a bit worried about throwing yesterday," Finch told reporters in Adelaide after a training session ahead of the first game in the city on Sunday.
"It didn't progress all that quickly but... the last three days it has been really good. I have got full movement ... I feel confident to go."
But short-form specialist Tye, who is usually deployed in the final overs, will take no part in the three-match campaign after injuring his right elbow fielding on Friday.
Finch said Tye picked up the injury throwing the ball.
"I think it was one of the first drills he did. He was a bit off balance and felt a bit of a pop in there," the captain said.
New South Wales quick Sean Abbott will replace him after the match on Sunday, which marks the return to T20 action of Warner and Steve Smith following their bans for ball-tampering.
The pair have already been welcomed back onto the Test and one-day teams.
Despite Tye's absence, Australia have plenty of bowling firepower at their disposal, including Mitchell Starc, Pat Cummins, Billy Stanlake and Kane Richardson.
After Adelaide, Australia face the Lasith Malinga-led Sri Lankans in Brisbane and Melbourne before Pakistan arrive for T20s in Sydney, Canberra and Perth.
The teams are all kick-starting preparations for the World Cup in Australia next year.
The Jamaican currently holds world records in the 100m, 200m and 4x100m with times of 9.58s, 19.19s and 36.84s respectively
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