Coming off a career-best year during which he became Australia's second highest-ranked player, 24-year-old Popyrin will join the team as a singles option alongside world No.12 Alex de Minaur.
Popyrin beat Swiss veteran Stan Wawrinka in the final of the Croatia Open in July, which was his second ATP Tour title, while he also scored three top-10 wins with his ranking rising from outside the top 100 in March to peak at world No.39 last month.
Jordan Thompson and Max Purcell are also in the mix for the second singles rubber while Purcell will link with his Wimbledon title partner Matt Ebden, who last week reached the semi-finals of the ATP Finals doubles competition with his Indian partner Rohan Bopanna.
Kokkinakis was forced to withdraw from the historic team tournament after a setback with an ankle injury.
"(Kokkinakis) played a tournament in Sydney a few weeks ago and twisted his ankle," Australia captain Lleyton Hewitt said in a statement.
"He was working through that, and then he had another little setback in training about a week ago."
Alexei Popyrin could play his first Davis Cup match for Australia in two years against the Czechs.
With in-form de Minaur spear-heading the Australian campaign, which opens against the Czech Republic on Wednesday (Thursday AEDT), Hewitt said he felt comfortable with the late change.
"To be honest, we had a lot of options, so I feel very comfortable with Alexei coming in," Hewitt said.
"He's had his career-best year on the ATP Tour this year, and we've got a lot of options in our singles but also in our doubles as well.
"Whoever we end up putting out there on the court I know is going to perform well and leave it all out there for us, and we've got full belief in all the boys."
Set to make his first Davis Cup appearance since November 2021, Popyrin is excited to be competing in the Spanish city of Malaga, where he used to live.
"No Spanish blood, but I did live here," Popyrin said.
"I lived in Alicante for five years where Demon (de Minaur) lives, and lived actually in Marbella for another five years.
"I'm kind of a local here now - most of my best friends are from this area, from Andalucia. It's basically a home tournament for me."
Last year, Hewitt's team were only denied at the final hurdle by Canada, who take on Finland with eight teams remaining in the competition.
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