The 23-year old New Zealand international has joined the Victory on a three-year deal from Russian side FC Alania.
"We are delighted to have Kosta on board with us at Melbourne Victory and he will add even more attacking flair to our team this season," Postecoglou said.
"Kosta has plenty of pace, great technical ability and is a proven scorer, having netted 12 goals the last time he played in the A-League.
"While he's only 23, he has made over 50 appearances at Brisbane Roar and Wellington Phoenix, so he's certainly aware of what is required to perform at this level, and I know he's excited to be returning to the A-League."
Apart from his time spent with the Phoenix, the Roar and Alania, Barbarouses had a spell on loan with Greek Super League outfit Panathinaikos.