By Paul Rincon
BBC News science reporter, in Washington DC
US researchers compared the rise in ocean temperatures with predictions from climate models and found human activity was the most likely cause.
In coming decades, the warming will have a dramatic impact on regional water supplies, they predict.
Details of the study were released at a major science meeting in Washington DC.
The conference is the annual gathering of the American Association for the Advancement of Science (AAAS).
"This is perhaps the most compelling evidence yet that global warming is happening right now and it shows that we can successfully simulate its past and likely future evolution," said lead author Tim Barnett, of the climate research division at the Scripps Institution of Oceanography in San Diego, California.
"If you take this data and combine it with a decade of earlier results, the debate about whether or not there is a global warming signal here and now is over at least for rational people."
Unless we know what we're dealing with, I think it's going
to be pretty hard to fix it
Dr Tim Barnett, Scripps Institution of Oceanography
They used several scenarios to try to explain the oceanic observations, including natural climate variability, solar radiation and volcanic emissions, but all fell short.
"What absolutely nailed it was greenhouse warming," said Dr Barnett.
This model reproduced the observed temperature changes in the oceans with a statistical confidence of 95%, conclusive proof - say the researchers - that global warming is being caused by human activities.
Regional water supplies will be dramatically affected by climate change in the decades immediately ahead, say the team.
The western US is already experiencing water shortages and research suggests that the region could face a water crisis within 20 years.
In the South American Andes and western China, millions of people could be left without adequate water during the summer due to accelerated melting of glaciers.
"If the snow pack melts sooner, and if societies don't have the ability catch all of that water, they're going to end up with water shortages in the summer," Dr Barnett explained.
According to the Scripps researcher, political leadership was now needed to avert a global disaster.
"Hopefully we can get the US cranked around in that direction. I think the first thing to do is figure out the global warming-related problems we have ahead of us around the world.
"Unless we know what we're dealing with, I think it's going to be pretty hard to fix it."