"Australia has always been a very welcoming country to such people from all around the world," Mr Morrison told reporters.
The move mainly affects Hong Kong citizens already in Australia, rather than those trying to flee.
Mr Morrison said the government would also try to attract Hong Kong-based businesses to Australia to create more jobs.
“I imagine that there will be many other countries in the region and around the world that would indeed be seeking to attract those businesses,” he said.
Britain has also extended residency rights for up to three million Hongkongers, allowing them to live and work in the UK for five years.
In May, the government said it expected Australia's overseas migration intake to shrink by more than 85 per cent on 2018-19 levels next financial year due to coronavirus travel bans.
Mr Morrison said Australia has also suspended its extradition agreement with the city.
The decision was an “acknowledgement of the fundamental change of circumstances” in Hong Kong because of the new security law, he said.
“Our view [is] that it undermines the one country, two systems framework, and Hong Kong’s own basic law and the high degree of autonomy guaranteed in the Sino-British Joint Declaration that was set out there.”
Canada has also suspended its extradition treaty with Hong Kong in the wake of the new security law.
Chinese foreign ministry spokesman Zhao Lijian strongly condemned the move to suspend the extradition treaty.
"The relevant remarks and measures announced by the Australian side seriously violate international laws and the basic norms governing international relations, and they are a gross interference in China's internal affairs," he warned.
"We urge Australia to immediately change course and stop interfering in Hong Kong and China's internal affairs by all means necessary, to avoid further damaging bilateral relations."
What exactly is Australia offering Hong Kong residents?
The arrangements for each type of visa will be slightly different.
For skilled and graduate visa holders, Australia will be extending visas by five years from Thursday, with a pathway to permanent residency at the end of those five years.
If you're a current or future student, you'll be able to stay for a total of five years once you've graduated, with a pathway to permanent residency at the end of that period.
If you're a temporary skilled visa holder, your visa will be extended by an additional five years from Thursday, with a pathway to permanent residency at the end of that period.
Also available will be a five-year temporary skilled visa with a pathway to permanent residency for future Hong Kong applicants, subject to meeting an updated skills list and appropriate market testing.
There will also be a focus on Hong Kong applicants to study and work in regional areas to help address skills shortages, with express pathways to permanent residency after three years.
Amnesty International Australia welcomed the decision to offer visas to Hongkongers currently in the country, but urged the government to grant protection to those in Hong Kong as well.
“We must also provide a safe pathway for Hongkongers who are currently in Hong Kong [and] who need to flee the horrific and harmful situation they face,” refugee adviser Graham Thom said.
“Australia has established precedents in stepping in to assist people suffering repression by extending visas and providing a pathway to protection, as the Hawke Government did notably in 1989 following the Tiananmen Square massacre.”
Updated travel advice
Earlier in the day, the Department of Foreign Affairs and Trade advised Australian citizens in Hong Kong to reconsider their need to remain there given the new “vaguely defined" security law.
In updated travel advice for the city, DFAT warned Australians could be at “increased risk of detention” and warned they could break the law “without intending to”.
“The new national security legislation for Hong Kong could be interpreted broadly. Under the law, you could be deported or face possible transfer to mainland China for prosecution under mainland law,” the updated advice reads.
“The full extent of the law and how it will be applied is not yet clear. You may be at increased risk of detention on vaguely defined national security grounds. You could break the law without intending to.
“If you’re concerned about the new law, reconsider your need to remain in Hong Kong.”
DFAT updated its travel advice for China on Tuesday, warning Australians they could be at risk of arbitrary detention.
China's foreign ministry said in response that "foreigners in China have absolutely nothing to worry about as long as they abide by the law".
Ministry spokesman Zhao Lijian told reporters that China hoped Australia would "remain objective and fair and do more to benefit the development of China-Australia relations".
Additional reporting AAP.