Milligan, capped 72 times for Australia, has previously led the side on 11 occasions, and first wore the captain's armband against South Korea in July, 2013.
"As we embark on a new era we look to leaders like Mark," Arnold said in a media release.
"Mark has been a part of the national team for 12 years now. The experience gained over that period is invaluable to our squad and his leadership on and off the park shines through every day."
The 33-year-old Milligan will lead the Socceroos against South Korea in a friendly in Brisbane later on Saturday before another Asian Cup warmup against Lebanon in Sydney next week.
Milligan, who plays for Scottish league club Hibernian FC, was selected for a fourth consecutive World Cup at Russia and beat out fellow central defender Trent Sainsbury, Arnold's son-in-law, for the captaincy.
"I am extremely humbled by the opportunity," said Milligan.
"We have had many great leaders over the years, who I both played alongside and admired as I grew up watching the national team.
"It is a huge honour to be joining them and I look forward to fulfilling the role with the support of our leadership group."
Australia defend their Asian Cup title at the United Arab Emirates in January.
(Reporting by Ian Ransom; Editing by Amlan Chakraborty)
