The Socceroos pulled off one of the more stunning moves in recent history by landing Volpato, who defected from Italy.
The Italy-based attacking midfielder will join the pre-camp in Los Angeles on Saturday morning, ahead of the international friendly against the World Cup co-hosts Mexico that night (Sunday AEST).
Volpato, who was born and raised in Sydney and played his junior football at Sydney United 58, Sydney FC and Western Sydney before moving to Italy, represented Italy at U19 and U20 level.
He famously knocked back Graham Arnold's pitch for him to join the Qatar 2022 squad and said in March he was "waiting for Italy", who subsequently didn't qualify for the World Cup.
Popovic in his pre-match press conference in Pasadena confirmed Volpato will be eligible to represent Australia at the Rose Bowl.
"It's not so much now trying to tick off who called who when, but he'd made his indication that he wants to play for Australia," Popovic said.
"We didn't chase him up, or (say) 'have you changed your mind? Can you come to the World Cup?'
"We've always appreciated him as a footballer. That hasn't changed, but I have to always respect the player's decision - and I've always done that.
"And once he made a decision that he wants to represent Australia, well, now there's a decision that we have to make: Do we go through the process? How quick can that process be? Is it worth doing now?
"And once putting everything together, we've come to the conclusion that we'll take that process further and fortunately that's all been ticked off.
"He's actually eligible to play tomorrow, which he may - he may sit on the bench and come on. So we'll see."
The 22-year-old has scored seven goals in his three seasons with Sassuolo after two seasons with fellow Serie A club Roma.
Volpato looms as the replacement for Riley McGree, who will miss the World Cup through a hamstring injury, and Popovic ruefully said he would have liked to pick both.
Popovic brushed aside a question about balancing the risk of bringing Volpato in so late.
"When you have a talented player, I'm not sure what the risk is," Popovic said.
"Yeah, we probably would have liked him to come in two or three days earlier, but he did play on the weekend, so the earliest he could have arrived was probably on Tuesday.
"... Would I have liked him to come four days earlier? Because that's the earliest I could have brought him anyway.
"I'd say yes, but the process was still happening, and I wanted a bit more clarity that this can actually go through in time that he's eligible for the World Cup.
"So I think that was my priority to make sure that that can happen. So I was willing to wait as long as I could, so that for me was the only risk."
Defender Harry Souttar, who chose to play for Australia over Scotland, said his teammates were looking forward to meeting Volpato.
"He's going to make us a better team, simple as that," Souttar said.
Popovic said he had a fit squad for the clash with Javier Aguirre's world No.15 - which also serves as the final audition before the squad is cut from 30 to 26 - with Aiden O'Neill having overcome an ankle injury.
The Rose Bowl, with a capacity of more than 75,000, will be packed with Mexico fans in a daunting pre-tournament test.
"It will really feel like we're here for the World Cup now," Popovic said.
