Brownfields Reauthorization Act of 2010 - Amends the Comprehensive Environmental Response, Compensation, and Liability Act of 1980 to: (1) include nonprofit organizations within the meaning of "eligible entity" for purposes of brownfields revitalization funding; (2) increase the limit on the maximum amount of a grant for brownfields remediation for each site; (3) authorize the President to transfer any duties under the brownfield remediation grant program to the Administrator of the Environmental Protection Agency (EPA); (4) revise eligibility requirements for brownfields revitalization funding; (5) require the Administrator to establish a program to provide multi-purpose grants to inventory, characterize, assess, conduct planning related to, or remediate brownfield sites in an area; (6) require the Administrator to establish a program to make competitive grants to be used at brownfield sites for projects that reduce environmental impact, increase community livability, and encourage sustainability; (7) authorize the Administrator to assign EPA employees to entities servings small, disadvantaged, or rural communities to build local capacity for the remediation and revitalization of brownfield sites in such communities; (8) increase and extend funding for brownfields revitalization; (9) require at least 7.5% of such funding to be used to carry out projects that reduce environmental impact, increase community livability, and encourage sustainability; and (10) increase and extend funding for state response programs established under such Act.