The Times Higher Education magazine’s table, based on a number of criteria, including teaching, research and staff and student mix, has Harvard top.
Only five British institutions are ranked among the top 50, with Cambridge and Oxford in joint sixth place.
However, last week a separate study in the UK ranked Cambridge as the world’s top university, followed by Harvard.
University leaders say the latest table indicates the UK still has the world’s second-strongest university system, but that this is under threat.
California Institute of Technology is ranked at number two in the table, with Massachusetts Institute of Technology in third place.
The only university outside of North America and the UK in the top 20 is the Swiss Federal Institute of Technology, in Zurich.
In the top 10, other than Cambridge and Oxford, the only non-US university is Imperial College London, in ninth.
Mainland China has six institutions in the top 200, more than any other country in Asia.
Only two Australian institutions are in the top 50, with seven in the top 200.
In the past, the Times Higher Education magazine had collaborated with the careers advice company QS to rank universities, but this year both organisations have produced separate lists, using different criteria.
Times Higher Education survey editor Phil Baty said a change to the way the tables had been compiled made comparisons over time difficult.
But he added: “We do contend, however, that these tables are realistic and so, in some cases, they may deliver an unpleasant wake-up call that the days of trading on reputation alone are coming to an end.”
David Willetts, UK Minister for Universities and Science, said: “Our universities have demonstrated their worth against new, more rigorous criteria.
“Reputation counts for less this time, and the weight accorded to quality in teaching and learning is greater.”
Professor Steve Smith, president of Universities UK, which represents vice chancellors, said: “The tables may show that the UK remains the second-strongest university system in the world, but the most unmistakeable conclusion is that this position is genuinely under threat.
“The higher education sector is one of the UK’s international success stories, but it faces unprecedented competition. Our competitors are investing significant sums in their universities, just when the UK is contemplating massive cuts in its expenditure on universities and science.
“Clearly, league tables must always come with a health warning as they never tell the whole story, but these rankings provide a useful indicator of international trends.
“This must serve as a wake-up call before big decisions are taken on university funding next month in the form of the government’s spending review and the recommendations of Lord Browne’s review into university funding and fees.”
This league table is one of many produced by organisations around the world.
According to a report earlier this year by the European Commission, 33 countries have some form of ranking system operated by government and accreditation agencies, higher education, research and commercial organisations, or the media.
The report says different systems favour different indicators, and the same indicators can be weighted differently by the various systems.
Experts have expressed “serious reservations” about the methodologies used by global ranking organisations, it says.
In the rankings released by QS last week, Cambridge was at the top, followed by Harvard.
The UK’s University College London, Oxford and Imperial College were all in the top 10.
1 – Harvard University
2 – California Institute of Technology
3 – Massachusetts Institute of Technology
4 – Stanford University
5 – Princeton University
6 – University of Cambridge
6 – University of Oxford
8 – University of California, Berkeley
9 – Imperial College London
10 – Yale University