World Cup-winner Romero was shown a straight red card during a tumultuous London derby against Chelsea a month ago in which Spurs ended with nine men and lost 4-1.
Romero's three-match suspension on top of serious injuries sustained by playmaker James Maddison and Romero's central defensive partner Micky van de Ven proved costly for Tottenham who have picked up one point from their last four games.
"It's great to have (Romero) back," Postecoglou told reporters on Wednesday. "He's the only recognised centre back we have fit at the moment with Van de Ven, Eric Dier and Ashley Phillips out. To have him as a recognised centre-back back in the team is good. He's a fantastic player but also a leader."
Romero has been sent off four times in 75 appearances in all competitions for Tottenham and while his pedigree is not disputed, his discipline has been called in to question.
"That is part of how he is as a player," Postecoglou said. "He brings physicality to the group, but obviously when he oversteps the mark that also affects the group negatively.
"I have had a word with him about the discipline side of things, but it is great to have him back."
Fifth-placed Tottenham could also have forward Richarlison back for the clash against West Ham with the Brazilian having recovered from a pelvic injury but Pape Matar Sarr is not quite ready, although he may return against Newcastle United on Sunday.
Postecoglou's side snapped a three-game losing sequence with a thrilling 3-3 draw at champions Manchester City on Sunday.
"So we were not overjoyed in getting a draw (at City) but the manner they went about it gave them more belief in what we are trying to be," Postecoglou said.
"The second-half performance showed real resilience, so it is more about the upturn in any feelings coming from that game rather than the result. We are now trying to keep focusing on hitting those levels."
Despite the recent run of results, the mood remains buoyant at Tottenham after Postecoglou led them to their best start after 10 games since the double-winning team of 1960-61.
West Ham manager David Moyes is a big fan of the Australian's style and is not surprised at the impact he has made in his first season as a Premier League manager.
"He's done remarkable. Tottenham are a really good side. He's made a big difference to what they do, how they play and the crowd and atmosphere," Moyes said.
"One thing that I would say is that I am surprised that everyone else has been surprised with what he has done after what he did at Celtic, where the pressure is enormous and he coped and dealt with it."
West Ham will again be without forward Michail Antonio but captain Kurt Zouma is available despite the trauma of having his house broken into last weekend before the home game against Crystal Palace.
"We are happy to have him back," said Moyes. "It's been a terrible situation for him and the club has supported him really well. He's our captain and we are fully behind him.
"No-one would want that to happen to themselves."
