Welfare support recipients who lose eight or more hours of work will also become eligible for payments of $200 per week.
"We have to push through this lockdown in Sydney," Mr Morrison told reporters.
"There is no other shortcut, there is no other way through. We have to just hunker down and push through."
People who lose work in Commonwealth-designated hotspots can currently qualify the COVID-19 Disaster Payment through Services Australia, when lockdowns extend beyond seven days.
The NSW government had been locked in negotiations with the federal authorities over the need for additional assistance in response to the economic impact of a four-week extension to restrictions.
The additional payment will only require affected persons to apply once, for the existing disaster payment.
Scott Morrison announces more financial support for NSW lockdown
NSW Premier Gladys Berejiklian said the additional support would help ensure people could rely on the payments throughout the lockdown.
"Please know we fought our guts out for these extra payments and I'm glad they are here and I do say they will keep us going. People should not feel stressed about their financial position," she said.
Source: GETTY IMAGES POOL
Mr Morrison has ruled out a return of the JobKeeper wage subsidy, describing it as "not the right solution for the problems we have now."
"What we are doing now is faster, it is more effective, it is more targeted, it is getting help where it is needed far more quickly," he said.
The new financial support arrangements will now be extended from week one of a lockdown in Australia.
Mr Morrison said the decision had been motivated by witnessing the effectiveness of restrictions in containing the threat of the Delta variant.
"It was very clear that this is now the pattern," he told reporters.
"There is a clear learning here, and that is the approach that I would expect states would follow in the future."
The COVID-19 disaster payment had previously been paid out at a maximum payment of $600 and minimum payment of $375.
Labor's health spokesperson Mark Butler described the federal government's repeated changes to the support payments as "chaotic".
"This chaotic approach by Scott Morrison chopping and changing the support arrangements every few days is a body blow to confidence and certainty for Australian businesses and workers," he told reporters.
More support for businesses
Meanwhile, additional financial support is also on the way for businesses affected by the Greater Sydney lockdown extended to 28 August.
The federal government has agreed to co-fund an expansion of the COVID-19 Business Support Payment in NSW.
Under the expanded payment, businesses - including not-for-profits - that have suffered a 30 per cent or more decline in turnover will now be eligible for between $1,500 and $100,000 per week.
The payment will continue to be calculated based on 40 per cent of the payroll for eligible businesses, but the maximum turnover threshold will be increased from $50 million to $250 million.
The payment for sole traders remains set at $1,000 per week.
NSW Treasurer Dominic Perrottet - who had been campaigning for a return to JobKeeper - described the increased federal support as a "marked improvement".
"I accept that I have probably been a pain in the arse for the prime minister," he said.
"But I am here to fight for workers and businesses across the state and I will continue to do that."
Sydney-based electrician Michael Pimm's business has taken a 42 per cent hit to its revenue amid the city's extended lockdown.
He said the restrictions have made him 100 per cent reliant on government support.
"More than ever now we need that support to come through as soon as possible," he told SBS News.
"We just need to find our way forward as I’m sure every business in NSW is doing right now."
Additional information around the business support can be found at Services NSW.