Almost 530 million children live in countries hardest-hit by high floods and tropical storms, mostly in Asia.
An additional 160 million kids are growing up in areas suffering severe droughts, mostly in Africa, UNICEF said in the report titled "Unless We Act Now."
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"The sheer number of children exposed to climate risk is alarming," said the report.
US President Barack Obama and China's Xi Jinping are joining more than 135 world leaders in Paris next week for an international conference aimed at clinching the first agreement on tackling global warming in 20 years.
The most urgent task is for world governments to agree on curbing greenhouse gas emissions, said Rees, but action is also needed on the national level to deal with the impact.
"When impacts occur, children must still be able to go to school and get the health care they need," he said.
A key concern is exposure to diseases that could become deadlier as a result of climate change and rising temperatures, including malaria, pneumonia, diarrhea and malnutrition.
Heatwaves, which have become more frequent, are causing more severe rashes, cramps, exhaustion and dehydration, which is a common cause of hyperthermia and death among infants and young children.
The impact of droughts on agriculture is leading to malnutrition and undernutrition, which is responsible for half of worldwide deaths of children under five.
Of the 160 million children who live in areas affected by severe droughts, almost 50 million are in countries where half or more of the population lives on less than four dollars per day.
Climate change makes existing inequalities worse, said Rees.
"A poor child and a rich child don't stand the same chances" when a flood or a drought hits, he said.
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