Inter and Jiangsu, who are owned by the same Chinese company, rushed through an agreement on Tuesday to send Sainsbury from China to Italy after Andrea Ranocchia had left the San Siro to join Hull City for the rest of the season.
The Socceroos centre-back was fully committed to a second season in the Chinese Super League but will attempt to settle quickly in Milan as he looks to make the most of the next six months at Inter.
Having joined Jiangsu just over a year ago from Eredivisie outfit PEC Zwolle, Sainsbury never thought he would be heading back to Europe now.
"I didn't expect to go back so quickly and I must admit to go to a club of this stature is a bit of a shock," he told the Daily Telegraph.
"I was thinking maybe I would go back to Holland and prove myself in European football again but this massive opportunity has come my way, one that I certainly couldn't turn down.
"It's the chance to play with and against some of the best players in Europe, in fact some of the best in the world. To go and pit myself against them will be a good fight — it's a short time period, so that allows me to give everything I possibly have until the end of the loan period and see where it takes me."
Realistically, three players - Miranda, Jeison Murillo and Gary Medel - are ahead of the Australia international in Inter's central defensive pecking order.
But with Miranda having been sent off in Inter's Coppa Italia loss to Lazio this week, Sainsbury could be in contention for game time when Stefano Pioli's side visit Serie A leaders Juventus on Sunday.
"I'm going to have to adjust very quickly, no doubt - European football is dog-eat-dog," Sainsbury said.
"But I don't want to go there just to make up the numbers or for the experience, I want to go all out to play."
Inter have won seven games in a row in the Italian top flight to sit fourth in Serie A, just five points behind second-placed Roma, with Juventus four points further ahead.