Speculation had been mounting Arnold could be sacked after failing to secure direct qualification to Qatar.
Lacklustre defeats to Japan and Saudi Arabia condemned Australia to third place in Group B of qualifying and sent them into the sudden-death playoffs.
But Football Australia has given Arnold, who is contracted until after this year's World Cup, a reprieve to lead Australia in the playoffs.
Australia will take on the United Arab Emirates, who finished third in group A, in Doha on June 7.
The winner of that one-off match will take on Peru in Qatar a week later for a spot in the World Cup.
Australia won just one of their past seven World Cup qualifying matches, including costly draws against China and Oman, but chairman Chris Nikou cited a need for stability before the playoffs.
"The board of Football Australia believed it was important that we provided a stable environment and to get on with planning for the play-off phase given the very short turn-around," Nikou said in a statement.
"By confirming that Graham will remain head coach of the Socceroos until the completion of our FIFA World Cup campaign, it enables Graham, his support staff and the playing group to move forward with certainty, and without delay, to ensure the best possible preparation for the next phase of qualification."
FA chief executive James Johnson was in Jeddah for Australia's 1-0 defeat to Saudi Arabia and will travel with Arnold to Doha for Friday's World Cup draw.
"Graham has Football Australia's support and after nearly four years in the role, still has the opportunity to finish the job he was appointed to in 2018 and see through his commitment to the national team," Johnson said in a statement.
"We now turn our sights to the difficult play-off stage in June, our final opportunity to qualify for the FIFA World Cup (in Qatar).
"As we have done throughout the campaign, we will work closely with Graham to ensure the team has the necessary resources, support and the approach required to achieve the best possible outcome and ultimately qualification to our fifth consecutive FIFA World Cup."