Signed with UK club Leicester, O'Connor posted a photo on social media organising his pet dog's transport before leaving for the airport with his wife Bridget.
He captioned the photo, "This is not goodbye... it's see you soon... hopefully... Bledisloe" and included a fingers crossed emoji.
"But for now the O'Connors have a flight to catch. All three of us."
The 68-Test veteran was initially due to join the Tigers following the British and Irish Lions series, but the 35-year-old stayed on for four Tests against South Africa and Argentina because of injuries in the play-making ranks.
In his return to the Test arena after a three-year absence, O'Connor proved a valuable addition.
He came off the bench to help the Wallabies overhaul the Pumas in Townsville, then almost repeated the feat in Sydney last Saturday.
O'Connor inspired a 19-point onslaught in the final quarter of an hour, but Australia's late revival fell short.
The Australian squad will be named this week for the two-Test Bledisloe Cup series against New Zealand, which doubles as part of the Rugby Championship.
Australia lead the championship on 11 points, one ahead of South Africa and New Zealand, who suffered a record defeat to the Springboks in Wellington over the weekend.
The squad is set to fly out on Monday for the September 27 clash against the All Blacks at Eden Park, meaning O'Connor would only have a few days on the ground in England.
However, coach Joe Schmidt has been non-committal about the future of 35-year-old O'Connor, with an eye on the future and his flyhalf stocks almost back to full strength.
Tom Lynagh is expected to be available following a hamstring strain and Ben Donaldson is back training after a thigh injury, while another youngster Tane Edmed had his first start at 10 last weekend.
Schmidt praised O'Connor's performance after the 28-26 loss to Argentina in Sydney on Saturday, but said no decision had been made on his participation.
O'Connor's last Bledisloe Cup match was in 2020 when New Zealand won the four-game series with two wins, a loss and a draw.
Teammates have endorsed O'Connor's involvement in the Wallabies' set-up, saying his experience had been invaluable.
"He backs himself, and that confidence that he brings, brings everyone with him as well," halfback Tate McDermott said.
"I think there's definitely a place for him long-term, 100 per cent."
After the Test at Eden Park, where the Wallabies haven't won since 1994 across 51 Tests, the teams square off in Perth on October 4.
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