Matt Wells has been promoted to assistant coach, replacing Chris Davies, who was named Birmingham City manager earlier this month.
Former Hibs manager Nick Montgomery and his assistant Sergio Raimundo have also joined. They both arrive as assistant coaches.
Postecoglou said: “I’m delighted that Matt has been appointed Senior Assistant Coach. He’s an outstanding young coach who has a great work ethic and attention to detail. He thoroughly deserves this opportunity.
“It’s also great to have Nick and Sergio join the Club, and they will add to the talented coaches we already have on the staff here.
“Both Nick and Sergio have a wealth of coaching experience over a number of years. They have already demonstrated a strong desire to both develop young talent and implement a football style that I believe will further strengthen the environment we have established. I’m looking forward to working with them.”