Cancer deaths, meanwhile, will likely rise from 8.2 million to 13 million per year as the world's population grows and ages and more people adopt risky lifestyle habits, said the report compiled by the International Agency for Research on Cancer (IARC).
It took aim at Big Tobacco, saying its sales drive was "inextricably linked" to a likely surge in lung cancer.
Released on the eve of World Cancer Day, the report was compiled by more than 250 scientists from over 40 countries. It is the first such overview in six years.
These nations are already grappling with poverty-associated cancers caused by infection or disease, she said.
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IARC director Christopher Wild said the focus should be on prevention.
"The particularly heavy burden projected to fall on low- and middle-income countries makes it implausible to treat our way out of cancer, even the highest-income countries will struggle to cope with the spiralling costs of treatment and care," he said.
New cases will likely rise to 19.3 million in 2025, with 11.4 million deaths, said Wild. By 2035, new cases would number about 24 million per year.
The report found a slight gender bias: 53 per cent of cancer cases and 57 per cent of deaths were among men.
In men, cancer most often attacked the lungs (16.7 per cent) followed by the prostate (15 per cent), colorectum (10 per cent), stomach (8.5 per cent), and liver (7.5 per cent).
For women, cancer was most common in the breast (25.2 per cent), colorectum (9.2 per cent), lung (8.7 per cent), cervix (7.9 per cent) and stomach (4.8 per cent).