Former New York City mayor and billionaire philanthropist Michael Bloomberg has spent hundreds of millions of dollars of his fortune over the past decade fighting tobacco use in the developing world. Now, with cigarette use declining globally, he is deepening his campaign.

Mr. Bloomberg is committing $360 million to be used between 2017 and 2022 to help raise tobacco taxes, implement smoke-free laws and pursue other strategies to curb tobacco use in low- and middle-income countries, according to Bloomberg Philanthropies, the...