The three teams will play each other in Jeddah in October, with the winner of the group advancing directly to the World Cup in the United States, Canada and Mexico.
Former Australia boss Arnold, who replaced Jesus Casas in May, will be attempting to steer Iraq to the World Cup for the second time after they made their debut at Mexico 1986.
"I have extensive experience working against both the Saudi and Indonesian national teams. I know their strengths, but I also know their weaknesses," Arnold said.
"But we are Iraq, an extremely proud nation with a higher FIFA ranking than both Saudi and Indonesia and we need to prove that."
Arnold's finest coaching achievement to date came at the 2022 World Cup when he led Australia to the last 16, with the Socceroos eliminated by eventual champions Argentina.
He resigned as Australia coach in September last year following a 0-0 draw with Indonesia in Jakarta.
The 61-year-old last faced Saudi Arabia in March 2022, when his Australia team lost 1-0 in a World Cup qualifier at the same King Abdullah Sports City Stadium where his Iraq team will face the Green Falcons on October 14.
"Having the belief in the players as I do, when we reach the crucial playoff matches in October, they will be in peak form, both physically and mentally ready to win," he said.
"I firmly believe this is our time and we will fight with everything we have to make the dream of millions of Iraqis come true."
The group runners-up will progress to a playoff for a berth in a series of intercontinental match-ups in March.
Australia overcame a poor start under Arnold to book their spot at the expanded 48-team World Cup with Tony Popovic in charge.
Regional heavyweights Japan, South Korea and Iran also secured berths in North America, along with first-time qualifiers Uzbekistan and Jordan.
