Romero is available for Thursday's home derby against West Ham having missed the previous three games after being shown a straight red card for a rash tackle on international team-mate Enzo Fernandez in the 4-1 defeat by Chelsea.
Spurs took just a point from their games without the Argentine and Postecoglou has backed him to keep his head in future.
"Great to have him back because he's the only recognised centre-half fit at the moment because Micky van de Ven, Eric Dier and Ashley Phillips are all out," the Spurs manager said of Romero on Wednesday.
"He's also a fantastic player, a leader in the group. We lost Madders [James Maddison] and him after the Chelsea game, so a lot of that [leadership responsibility] fell on Sonny's [Heung-min Son] shoulders. So from that perspective, it's good to have him back.
"I've not had to have a word with him about discipline. It’s part of who he is as a player, he brings a physicality to it.
"When he oversteps the mark the whole group pays a price so it's up to him to maintain the discipline I know he can show.
"But more importantly, he's such a strong presence on the field and during the week so good to have him back.
"His training has been good but he's been frustrated because not just the fact he has missed out but he has understood the situation we've been in.
"It was not like he was the only one missing. All of a sudden post-Chelsea we lost Micky, we lost Destiny [Udogie], we lost pretty much our whole back four, we lost Madders and he knows how important he is.
"He was frustrated and he had the international week which was good for him because he got a couple of games in there, but he's been ready to go. The last week he has trained really well and I know he is happy and I know the rest of the group are happy to have him back in."
Postecoglou was without 11 players - 10 due to injury and the suspended Romero - for Sunday's 3-3 draw at Manchester City but Spurs' selection crisis is beginning to ease slightly, with Pape Sarr expected back this week and Richarlison making a late cameo at the Etihad Stadium.
But Postecoglou revealed that Eric Dier has now joined the list of absentees after going down with a groin problem.
"Pape is back training, probably tomorrow will be a bit too soon for him but Sunday [against Newcastle] I'm pretty sure he'll be available," Postecoglou said. "Richy got five minutes the other day and felt short physically, but in terms of where he is he's available. All the rest I don't expect to see back for a while.
"Dier hasn't trained for over a week now and we're working on the issue so I assume when he does get back he'll need a bit of time. It's a groin issue."
Maddison this week described his recovery from ankle ligament damage as a "slow burner", but Postecoglou played down fears the playmaker will be sidelined for even longer than anticipated.
"I'm not sure about James' medical qualifications, whether we should go with his diagnosis," he said.
"I'll leave it to the medical team. As far as I know, it's going along OK."
"I'm not sure about James' medical qualifications... as far as I know, it's going along OK"
Ange Postecoglou on James Maddison's injury recovery
Spurs' fringe players have stepped up during what Postecoglou described as their "tough period", with full-backs Emerson Royal and Ben Davies deputising at centre-back, Giovani Lo Celso scoring in consecutive matches and Bryan Gil starting back-to-back League games for the first time for Spurs.
"I was always heartened by training every day, guys like Gio and Bryan Gil, and even Ben Davies who hasn't had a lot of game time," the Australian said. "They've been training well and Emerson has been training well.
"We're obviously asking them to do a little bit of a different role, and that's another challenge but again I come back to their application and determination to play our football, which has been key to that.
"Wolves aside, our level of performance has been pretty good considering what we've had to go through so far."