Australia's Mitch Marsh dropped from the side
Also axed from the 13-man squad after the humbling 2-1 series defeat to India were underperforming opener Aaron Finch and middle-order batsman Peter Handscomb.
In-form Joe Burns was recalled for the first time since the South Africa tour early last year and could open the innings with rookie Marcus Harris, who did enough against India to keep his place.
But they face competition from Matt Renshaw, who has been handed another opportunity despite misfiring in the domestic Sheffield Shield this season.
Allrounder Marnus Labuschagne was retained from the team that played the rain-affected drawn Test in Sydney this week, as was Travis Head.
Selectors also kept faith with their pace attack of Mitchell Starc, Josh Hazlewood and Pat Cummins, with veteran Peter Siddle also included.
National selector Trevor Hohns said "there is no doubt the India series produced some disappointing results" and change was needed, after four Tests characterised by the failure of any Australian batsmen to score a century.
"Ultimately Aaron, Peter, Shaun and Mitch have not produced the performances expected of them with the bat at the Test level," he said.
"They have been given a good opportunity, but have not produced the scores we need."
He added, however, that the door was not closed and they must now prove themselves again in domestic cricket and the one-day series against India this month.
Pucovski was the surprise call-up.
The 20-year-old is one of the brightest batting talents in the country, scoring a double century for Victoria last year - the first Australian under 21 to do so since Ricky Ponting.
But he has only played eight first-class matches, and after that double ton took a break from cricket because of a mental health issue.
"Will Pucovski is an exciting young player who is making his mark in the Sheffield Shield. He is another player with a track record of making centuries," said Hohns.
Despite his relative inexperience, Pucovski said he was ready to step up.
"It is every kid's dream. To think that in two weeks time there is a chance I would play for my country is amazing. I can't use words to describe it," he told reporters.
"I can't wait to get up there and in amongst it."
Burns, who has played 14 Tests, has been knocking on the door this season with Queensland, while Renshaw has been unlucky not to get another call-up until now, since his last appearance at Johannesburg in 2018.
"We see him as a long-term prospect as a Test player and have confidence in his ability to bounce back following a string of low scores early in the Shield season," said Hohns of the 22-year-old.
Renshaw, who has a century and three 50s from his 11 Tests, said he wanted to emulate the exploits of India's rock-solid number three Cheteshwar Pujara.
"Everyone talks about (Virat) Kohli and (Ajinkya) Rahane, but Pujara was unbelievable and showed how good he was mentally to bat for so long," he said.
Burns, Renshaw and Pucovski will all play for a Cricket Australia XI in a pink-ball match against Sri Lanka ahead of the Tests in preparation for the day-nighter in Brisbane from January 24. The second Test is in Canberra from February 1.
Australia squad: Joe Burns, Pat Cummins, Marcus Harris, Josh Hazlewood, Travis Head, Usman Khawaja, Marnus Labuschagne, Nathan Lyon, Tim Paine (capt), Will Pucovski, Matt Renshaw, Mitchell Starc, Peter Siddle
Cricket Australia XI: Joe Burns (capt), Kurtis Patterson, Scott Boland, Jake Doran, Jon Holland, Marnus Labuschagne, Michael Neser, Will Pucovski, Jason Sangha, Matt Renshaw, Chris Tremain