Arnold, who led the Central Coast Mariners to the 2012/13 A-League title, replaces Frank Farina who was sacked after the team was knocked out in the opening week of this season's play-offs.
The 50-year-old comes with a wealth of experience. He was acting national coach at the 2007 AFC Asian Cup as well as an assistant coach to Guus Hiddink and Pim Verbeek during the 2006 and 2010 FIFA World Cups™.
He takes charge after parting company with Vegalta Sendai last month following a poor start to the J-League season.
Reports said he signed a AUD$1.8 million (USD$1.7 million) deal that will make him the best-paid coach in the A-League.
"I am extremely excited to be here. It has always been my dream as a Sydney boy to coach Sydney FC, in my view the biggest club in the country," Arnold said.
"It's a fantastic opportunity and I'm looking forward to working with the players and coaching Sydney FC to consistent domestic success and Asian Champions League qualification."
Sydney have won the A-League twice under German Pierre Littbarski (2005/06) and Czech Vitezslav Lavicka (2009/10), but have generally underachieved before moderate crowds in the nine seasons of the domestic championship.
"Graham is one of the A-League's most successful coaches and has a proven track record of producing high quality, winning football teams," Sydney chairman Scott Barlow said.
"He brings to the head coach's role a wealth of international and Asian Champions League experience and as a former Socceroos coach, has dealt with the demands of coaching a high profile team."
Arnold will be looking to rebuild the club following the recent departure of highly-paid Italian superstar Alessandro Del Piero.
As a player, Arnold represented his country 54 times and played 453 club games in Australia, Belgium and Japan.