The National Governors Association Center for Best Practices awarded the grants on Thursday.
The money is earmarked for the development of strategies and laws, and the analysis of existing programs aimed at fighting childhood obesity.
States getting the grants include Kentucky, Michigan, Minnesota, Mississippi, New York, Rhode Island, South Dakota, Tennessee, Virginia and West Virginia.
"The challenge for states is to develop interventions that have the greatest impact on childhood obesity, and these awards will help states in their planning efforts," said John Thomasian, director of the NGA Center.
The National Governors Association Center, based in Washington, D.C., helps governors and their staffers develop public policy. It is funded by dues from states and by public and private grants.