A lifelong Indianapolis resident, Peterson graduated from Purdue University and the University of Michigan Law School. He returned to Indianapolis to practice law for several years before joining the staff of Governor Evan Bayh, eventually serving as Chief of Staff. Peterson became Indianapolis' first democratic mayor in 33 years when he took office on January 1, 2000.
Peterson was re-elected in 2003. During his second term, he led the efforts to consolidate city and county government, merging the Indianapolis Police Department with the Marion County Sheriff's Department. He oversaw plans to construct Lucas Oil Stadium and expand the Indiana Convention Center and attracted additional development to downtown, including the Simon Property Group headquarters and Conrad Hotel.
He established the Peterson Fellows program at the School of Public and Environmental Affairs (SPEA) at IUPUI in 2016, which provides a one-year paid internship for a SPEA graduate student who has a career interest in public service. In 2017, Peterson was appointed chair of Indiana University's Center for Global Health development board, leading the advocacy and fundraising efforts for IU's global health partnerships, such as the Academic Model Providing Access to Healthcare (AMPATH). He currently serves as CEO of Christel House International.