The 60-year-old returned to the Premier League on Wednesday, just three months after leaving Tottenham, as he replaced Nuno EspÃrito Santo at the City Ground. Forest, who are back in European competition for the first time in over 30 years, believe Postecoglou's attacking philosophy can take the club to new heights.
Postecoglou, who guided Spurs to Europa League success in May, their first trophy in 17 years, said he was relishing the challenge of leading a club with Forest's tradition.
"I love winning things. That's what I've done throughout my career," he said in an interview with the club's media.
"It's no secret I like my teams to attack and score goals. People sometimes think it's just about style, but for me it's about winning matches and bringing success."
He added: "When you look at what the club has achieved in recent times, it's remarkable. Many promoted clubs struggle, but Forest are back in Europe so quickly and competing for honours. That speaks volumes about the ambition here. I sense the club wants more, and I'm determined to make sure Forest take their rightful place among the top clubs."
The Australian has often spoken about watching European Cup finals with his father in Melbourne, and he is acutely aware of Forest's golden era under Brian Clough, when the club won back-to-back European Cups in 1979 and 1980. "It's a fantastic club with great history. That responsibility excites me, and I can't wait to get started," he said.
Postecoglou has also reunited much of his trusted backroom staff. Former Celtic captain Mile Jedinak, ex-Hibernian boss Nick Montgomery and Sergio Raimundo have all joined as assistant coaches, while Rob Burch, who worked with him at Tottenham, has been appointed goalkeeper coach.
Forest have begun the new campaign strongly, reaching the Europa Conference League group stage after beating Partizan Belgrade in the play-off round. Club officials have said the appointment of Postecoglou underlines their intent to keep building momentum both domestically and in Europe.
Chairman Evangelos Marinakis has publicly backed his new manager, describing him as "a proven winner with the mentality to match the ambitions of this football club".