A new route between Sydney and New Delhi will launch on 6 December with three flights a week.
Sydney to Singapore flights will resume on 23 November, four weeks earlier than scheduled, operating three days a week before ramping up to daily before Christmas.
Sydney to Fiji will be brought forward to 7 December for four flights a week.
Qantas will fly from Sydney to Johannesburg three times a week from 5 January, three months earlier than scheduled.
From 14 January, the airline will resume its Sydney to Bangkok services more than two months earlier than expected, while Jetstar flights to Phuket will start on 12 January.
Sales on already announced Qantas flights to London and Los Angeles have been strong, with some selling out in hours after the border announcement.
Mr Joyce said it was big news for Australia in the wake of the coronavirus pandemic which began in early 2020.
"This 20 (past) months is probably the darkest period in Qantas' 100-year history," he told reporters at Sydney Airport.
"It has meant we have had to ground aircraft, stand down people and restructure the business. But there is light at the end of the tunnel.
"It is very clear that because Australians have rolled up their sleeves and taken the jab, we can see that light."
Flights to Honolulu, Vancouver, Tokyo and New Zealand are still scheduled to commence from mid-December 2021, with other destinations to restart in the new year.
All travellers will have to be fully vaccinated and will be required to test negative for coronavirus within 72 hours of departure.
Mr Morrison also announced the government is in the final stages of securing a travel bubble with Singapore.
"We anticipate that being able to be achieved within the next week or so, as we would open up to more visa class holders coming out of Singapore," he said.
The prime minister said those arrangements are expected to align with when Qantas resumes flights there.
With Emma Brancatisano.