The projection from the Organisation for Economic Co-operation and Development (OECD) shows a far-reaching shift in the balance of graduate numbers, with the rising Asian economies accelerating ahead of the United States and western Europe.
The forecasts for the shape of the "global talent pool" in 2020 show China as rapidly expanding its graduate numbers - set to account for 29% of the world's graduates aged between 25 and 34.
The biggest faller is going to be the United States - down to 11% - and for the first time pushed into third place, behind India.
The US and the countries of the European Union combined are expected to account for little more than a quarter of young graduates.
Russia is also set to decline - its share of the world's graduates almost falling by half since the beginning of the century.
Indonesia, according to the OECD's projections, will rise into fifth place.
Is this an end-of-empire moment?
Higher education has become the mirror and magnifier of economic performance - and in the post-World-War-II era, universities in the US, western Europe, Japan and Russia have dominated.
The US in particular has been the university superpower - in wealth, influence and until recently in raw numbers.
Up until 2000, the US still had a share of young graduates similar to China. And Japan had as big a proportion of young graduates as India.
Now China and India are the biggest players.
Their rise in graduate numbers reflects their changing ambitions - wanting to compete against advanced economies for high-skill, high-income employment.
Instead of offering low-cost manufacture, they are targeting the hi-tech professional jobs that have become the preserve of the Westernised middle classes.
As the OECD figures show, this is not simply a case of countries such as China expanding while others stand still.
Across the industrialised world, graduate numbers are increasing - just not as quickly as China, where they have risen fivefold in a decade.
The OECD notes that by 2020, China's young graduate population will be about the same as the total US population between the ages of 25 and 64.
This changing world map will see Brazil having a bigger share of graduates than Germany, Turkey more than Spain, Indonesia three times more than France.
The UK is bucking the trend, projected to increase its share from 3% in 2010 to 4% in 2020.
This push for more graduates has a clear economic purpose, says the OECD's analysis.
Shifting from "mass production to knowledge economy occupations" means improved employment rates and earnings - so there are "strong incentives" for countries to expand higher education.
But will there be enough graduate jobs to go round?
The OECD has tried to analyse this by looking at one aspect of the jobs market - science and technology-related occupations.
These jobs have grown rapidly - and the report suggests it is an example of how expanding higher education can generate new types of employment.
These science and technology jobs - for professionals and technicians - account for about four in every 10 jobs in some Scandinavian and northern European countries, the OECD suggests.
In contrast - and showing more of the old order - these technology jobs are only a small fraction of the workforce in China and India.
The OECD concludes that there are substantial economic benefits from investing in higher education - creating new jobs for the better-educated as unskilled manufacturing jobs disappear.
The OECD forecast reveals the pace of growth in graduate numbers. But it does not show the quality or how this expansion will translate into economic impact.
There are other ways of mapping the changing distribution of knowledge.
A team at the University of Oxford's Internet Institute has produced a set of maps showing the "geography of the world's knowledge".
This measures how populations are consuming and producing information in the online world - mapping the level of internet use, the amount of user-generated material in Google, concentrations of academic activity and the geographical focus of Wikipedia articles.
And in contrast to the rise of the Asian economies, this tells a story of continuing Western cultural dominance.
"In raw numbers of undergraduates and PhDs, the Asian economies are racing ahead," says Prof Viktor Mayer-Schonberger, from the Oxford Internet Institute.
"But what's interesting is how the West persists in its positions of strength - because the West controls the institutions.
"There are more students in China than ever before - but they still use Western mechanisms to publish results, they accept the filters," says Prof Mayer-Schonberger.
"The big question will be whether the Chinese researchers can be as insightful as their Western counterparts - we don't know yet."
The maps also reveal how much Africa and South America are losing out in this new scramble for digital power.
Prof Mayer-Schonberger said he was "completely shocked" at the extent of the imbalance.
Another feature of the Oxford study is to show how research bases and their spin-out economic activity are clustered into relatively small areas.
In the US, says Prof Mayer-Schonberger, there is hugely disproportionate investment around Silicon Valley and the Boston area, with large tracts of "wasteland" between.
"Each era has its own distinct geography. In the information age, it's not dependent on roads or waterways, but on bases of knowledge.
"This is a new kind of industrial map. Instead of coal and steel it will be about universities and innovation."
By the end of this decade, four out of every 10 of the world's young graduates are going to come from just two countries - China and India.