Africa, home to 15 of the 20 most vulnerable countries, is the region most at risk from climate change, the report says.
Other areas threatened by global warming include south Asia and small island developing states.
The study warns that the true human impact of global warming is likely to be far more severe than it predicts, because it uses conservative UN scenarios.
About 325 million people are seriously affected by climate change every year, the report estimated, warning this will more than double in 20 years to 10 per cent of the world's population, currently at about 6.7bn.
Economic losses due to global warming amount to more than $125bn - larger than the flow of aid from rich to poor nations - and are expected to rise to $340bn each year by 2030, according to the report.
Developing countries are said to bear more than nine-tenths of the human and economic burden of climate change, while the 50 poorest countries contribute less than one per cent of the carbon emissions that are heating up the planet.
Annan urged countries due to meet at UN talks in Copenhagen, the Danish capital, in December to agree on an effective, fair and binding global pact to succeed the Kyoto Protocol, the world's main mechanism for tackling global warming.
"Copenhagen needs to be the most ambitious international agreement ever negotiated," Annan wrote in an introduction to the report.
"The alternative is mass starvation, mass migration and mass sickness."
New scientific evidence points to greater and more rapid climate change.