The August signing from Dutch club VVV Venlo has struggled for fitness and pulled a calf muscle while warming up ahead of the Premier Sports Cup clash with Raith Rovers last month.
Much is expected from Giakoumakis after finishing top scorer in the Eredivisie last season even though his club were relegated.
Postecoglou admitted there were fears he might break down again while doing intensive training work over the international break. However, the manager has reported that all is well.
The striker has been added to the striker options at Postecoglou's disposal and he could feature against Motherwell at Fir Park, where Celtic hope to secure a successive away win in the league.
The Parkhead side are currently sixth and could do with Giakoumakis making a strong start to his Celtic career as Albian Ajeti continues to struggle to offer convincing evidence that he’s the long-term answer in attack.
The manager is relishing the prospect of having Giakoumakis available.
“He is the one who benefited the most from the international break,” said Postecoglou. “He missed pre-season and the start of the season. Then he had 10 days' quarantine so he was really under done.
“We were kind of holding our breaths to get him through to this break and I think he feels a lot better in himself.
“He feels ready to make an impact now. That’s great for us.
“We have him, Ajeti, obviously Kyogo, Jota, Abada, there’s Mikey Johnston now available and James (Forrest) on the way. We have good attacking options to start and on the bench. We’ll be in good shape.”