The 33-year-old signed a two-year deal with Hibs on August 18 but red tape had so far prevented him from teaming up with his new club.
Milligan has been called up to Australia’s training camp in Turkey during the international break, along with Easter Road team mate Jamie Maclaren, but is free to begin training and playing for Hibs on his return.
The 71-times capped international could make his debut for Hibs against Kilmarnock on September 15.
Milligan’s imminent arrival will come as a huge relief to head coach Neil Lennon, who has had to deploy Steven Whittaker, a natural defender, in the holding role since losing Marvin Bartley to injury in the 3-0 loss to Molde in the Europa League third qualifying round.
Speaking last month, Lennon said: “We need physicality. Mark will bring that. He is athletic. He is very experienced. He had a good World Cup, “I like his composure on the ball and he is a big boy and can get around the pitch.”