Most of the two dozen nations that have passed this tipping point -- including Australia, Sweden, France, the United States and Britain -- are enjoying modest baby booms, breaking a pattern of declining fertility that has held for decades if not longer.
If the trend holds for these and other countries moving up the socio-economic ladder, it could have huge and largely positive implications for what have been up to now rapidly ageing societies, the researchers said.
The US Census Bureau estimated last month that the number of persons on the planet over 65 years old will double from just over 500 million today to 1.3 billion in 2040.
"Our findings are highly relevant in the debate on the future of the world's population ... and provide a different outlook for the 21st century," notes the study, published in the British science journal Nature.
The myriad problems stemming from sagging birthrates -- increased health costs for the elderly supported by a shrinking workforce -- had seemed to be the inevitable price to pay for higher incomes and longer lifespans.
Most well-off nations have long since slipped below the fertility rate needed simply to maintain a stable population, an average of 2.1 children per woman.
If unchanged, the 2005 birthrates of countries such as South Korea, Japan, Italy and Spain -- 1.08, 1.26, 1.32 and 1.33, respectively -- will, in the absence of immigration, halve each nation's population in 40 to 45 years.
The further these and other countries advanced along a widely used measure of social progress called the Human Development Index (HDI), earlier studies showed, the fewer babies were born per woman.
The HDI scale takes into account life expectancy, GDP per capita and literacy rates, and runs from zero to 1.0.
The 20 lowest placed countries -- all in Africa -- score from 0.30 to 0.48, and the 20 highest score from 0.93 to 0.97.
A trio of researchers led by Mikko Myrskyla of the University of Pennsylvania in Philadelphia analysed recent data from most of the world's nations to see if any new trends had emerged.
What they uncovered was "a fundamental change in the well-established negative relationship between fertility and development."
On average, national birthrates begin to bottom out when the HDI hits about 0.86, and climb again when the development index approaches 0.95, they found.
The 12 nations highest on the index averaged just over 1.8 births per women in 2005, and in some cases the rate has continued to climb since then.
In 2008 France, for example, topped 2.0 for the first time in at least 40 years.
Changes in society that make it easier for women to choose to have children are a key driver behind the rich nation baby boom, the study suggests.
More advanced degrees, a large presence in the workforce, higher incomes -- "these changes make it likely that women, and couples, will find it easier to pay the high economic price of having children," notes Stanford University professor Shripad Tuljapurkar in a commentary, also in Nature.
Interestingly, the same kind of social and economic advances for women have been critical in helping to lower fertility rates in very poor countries where five or six children per women is still the norm.
Japan and South Korea would appear to be exceptions to the new findings, but the fact that both countries rank high on the HDI scale but have among the lowest fertility rates in the world may underscore the relatively unchanging status of women in both societies, the authors suggest.
But other anomalies such as Canada and Germany, whose birthrate lags behind similarly rich nations, have yet to be explained.