Researcher Katharine Betts from Swinburne University also found that a reorientation of the migration program away from family reunion towards skilled migration and restrictions on new migrants' access to welfare contributed to the change.
"It is remarkable that this change should have taken place during a period when the number of immigrants, after an initial lull, increased sharply," the study says.
The shift in attitude comes despite criticism of the Coalition's migration policies, which has resulted in splits within the Liberal Party, notably on border-protection issues.
The study, to be published in the next edition of the People and Place journal, described a "considerable softening" in opposition to immigration between 1996 and last year. During that period, opposition dropped by more than 20 percentage points to less than 40 per cent and support rose from single figures to almost a quarter by 2001.
A slight falling away of support last year was not statistically significant and might be due to sampling variation, Ms Betts said.
Australia's overall migration program has steadily increased over the past decade. The Immigration Department has planning levels for 2005-2006 at 130,000 to 140,000 places.
Ms Betts said the public's "ignorance" and a mistaken belief that migration was a remedy for an ageing population had driven the change in sentiment.
"While immigration can do a great deal to make the population larger, it can do very little to offset demographic ageing," Ms Betts said.
"One probable reason for the shift in public attitudes to immigration is public ignorance about the size of the intake and its demographic implications."
Fertility is a far more effective way to combat an ageing population, an idea reflected by Peter Costello when the federal Treasurer urged people to have larger families in the 2002 Intergenerational Report and by former Victorian premier Jeff Kennett, who in 1999 encouraged a group of high school girls to do the same.
The study found that anxiety about the ageing population was higher than previously thought, with more than 22 per cent of voters nominating it as a concern.
Ageing polled only slightly lower than hospitals, healthcare and high taxation as a concern.
The study also found that older people were less supportive of migration than younger people, while Labor voters were less supportive than Liberal voters.
But anxiety about ageing had softened opposition to migration in the two groups.
"Concern about ageing may have weakened opposition to immigration among two segments of the electorate which would have otherwise been less likely to change their views -- older people and Liberal voters," the study found.
Ms Betts analyzed data from the Australian Election Studies Surveys and Australian Surveys of Social Attitudes.