The World Meteorological Organisation's annual assessment said 2013 was the sixth-warmest year on record. Thirteen of the 14 warmest years have occurred in the 21st century.
Rising sea levels are leading to more damage from storm surges and coastal flooding, the agency's secretary-general Michel Jarraud said.
Typhoon Haiyan, which struck in November, killed at least 6100 people and caused billions of pounds worth of damage in the Philippines and Vietnam.
Australia, meanwhile, had its hottest year on record.
Mr Jarraud said: "Many of the extreme events of 2013 were consistent with what we would expect as a result of human-induced climate change."
He also cited other costly weather disasters, such as the £13bn of damage from flooding in Europe in June and £6bn caused by Typhoon Fitow in China and Japan.