Video report by ITV News Correspondent Dan Rivers
But the rain brought challenges for fire crews as they attempted to complete strategic burns in preparation for higher temperatures forecast for later in the week.
Australia’s wildfires, which began in September, have so far scorched an area roughly the size of Croatia, killing at least 24 people and destroying some 2,000 homes.
"The fires are still burning. And they'll be burning for months to come," Morrison said.
"And so that's why I outlined today that this is an initial, an additional, investment of $2 billion. If more is needed and the cost is higher, then more will be provided."
Eerie footage shows the red glow of the wildfires as an Australian Air Force plane attempted to land in Mallacoota, a coastal town in Victoria.
Residents have been cut off for days, with thousands of people sheltering on beaches to escape the fires.
Heavy smoke hampered the evacuation effort and around 300 people were still waiting to be evacuated on Monday.
Several Hollywood stars used the Golden Globes awards to express their support for Australia as the fires continue, with some saying the situation was more clear proof of the need to do more to fight climate change.
More than 135 fires were still burning across New South Wales (NSW), Australia’s most populous state, including almost 70 that were uncontained.
The Rural Fire Service warned the rain would not put out the largest and most dangerous blazes before conditions deteriorated again this week.
"With the more benign weather conditions it presents some wonderful relief for everybody, the firefighters, the emergency services personnel, but also the communities affected by these fires," Shane Fitzsimmons, commissioner of the New South Wales Rural Fire Service, told reporters.
"But it also presents some real challenges when it comes to implementing tactical and strategic back-burns and other techniques to try and bring these fires under control."
At least 200 millimetres (8 inches) of rain would need to fall over a short period of time in order to snuff out the fires - around 20 times what has fallen across the region in the past day.
Officials warned the country's wildfire season, which generally lasts through March, was nowhere near its end.
Australia’s capital, Canberra, had the worst air quality of any major city in the world on Monday morning owing to smoke from nearby wildfires.
The Department of Home Affairs, which is responsible for coordinating the country’s response to disasters, told all non-critical staff to stay home because of the abysmal air quality.
The fires have evolved as something of a public relations disaster for Australian Prime Minister Scott Morrison.
Mr Morrison announced on Saturday he would dispatch 3,000 army, navy and air force reservists to help battle the fires. He also committed $20 million AUD (£10.6 million) to lease firefighting aircraft from overseas.
But the moves did little to tamp down criticism that he was slow to act, even as he has downplayed the need for his government to address climate change, which experts say helps supercharge the blazes.
Australians know to expect summer wildfires. But the blazes arrived early this year, fed by drought and the country’s hottest and driest year on record.
Scientists say there’s no doubt man-made global warming has played a major role in feeding the fires, along with factors like very dry vegetation and trees, and strong winds.
Mr Morrison, chided for past remarks minimising the need to address climate change, has deflected criticism while trying to change his tone.
He has faced widespread criticism for taking a family vacation in Hawaii at the start of the wildfire crisis, as well as for his sometimes distracted approach as the disaster has escalated and his slowness in deploying resources.
His handling of the deployment of reservists also came in for criticism. Commissioner Fitzsimmons, who is leading the fight in NSW, said he learned of the deployment through media reports.
“It is fair to say it was disappointing and some surprise to hear about these things through public announcements in the middle of what was one of our worst days this season, with the second-highest number of concurrent emergency warning fires ever in the history of New South Wales,” he said.
Mr Morrison was also forced to defend a video posted on social media Saturday that promoted the deployment of reservists and the government’s response to the wildfires.
At the Golden Globes, messages of support for Australia came from stars including Ellen DeGeneres, Patricia Arquette and Australian-born Cate Blanchett.
Russell Crowe, New Zealand born but a long-term Australian resident, could not attend as he was home helping take precautions against the fires.
Winning a Golden Globe for his role in The Loudest Voice, Crowe sent a message which was read out on stage by Jennifer Aniston.
It said: “Make no mistake, the tragedy unfolding in Australia is climate change-based. We need to act based on science, move our global workforce to renewable energy and respect our planet for the unique and amazing place it is. That way, we all have a future. Thank you.”
The view from the ground: ITV News Correspondent Dan Rivers explains the challenges facing Australians
With wildfires ravaging an area around three times the size of Wales, thousands of Australians are in danger and hundreds of millions of animals have died.
ITV News Correspondent Dan Rivers has been in Australia witnessing the devastating impact of the wildfires, and explains how communities, emergency services, and wildlife are being affected: