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The 2016 Global Nutrition Report said 44% of countries were now experiencing "very serious levels" of both under-nutrition and obesity.
It means one in three people suffers from malnutrition in some form, according to the study of 129 countries.
Being malnourished is "the new normal", the report's authors said.
Malnutrition has traditionally been associated with children who are starving, have stunted growth and are prone to infection.
These are still major problems, but progress has been made in this area.
The report's authors instead highlighted the "staggering global challenge" posed by rising obesity.
The increase is happening in every region of the world and in nearly every country, they said.
Hundreds of millions of people are malnourished because they are overweight, as well as having too much sugar, salt or cholesterol in their blood, the report said.
Professor Corinna Hawkes, who co-chaired the research, said the study was "redefining what the world thinks of as being malnourished".
"Malnutrition literally means bad nutrition - that's anyone who isn't adequately nourished.
"You have outcomes like you are too thin, you're not growing fast enough… or it could mean that you're overweight or you have high blood sugar, which leads to diabetes," she said.
While many countries are on course to meet targets to reduce stunted growth and the number of underweight children, very few are making progress on tackling obesity and associated illnesses such as heart disease.
In fact, the report says, the number of children under five who are overweight is fast approaching the number who are underweight.
Co-chairman Lawrence Haddad said: "We now live in a world where being malnourished is the new normal.
"It is a world that we must all claim as totally unacceptable."
The report calls for more money and political commitment to address the problem. It says for every $1 (70p) spent on proven nutrition programmes, $16 (£11.25) worth of benefits ensue.