Kenney, 57, succeeds outgoing Mayor Michael Nutter, who leaves office after two terms. Kenney served on City Council for more than two decades before he was elected in November.
He was joined on the stage of the Academy of Music by his daughter and son, and was sworn in by newly elected state Supreme Court Justice Kevin Dougherty.
Kenney said he was humbled that Dougherty, a neighborhood friend from South Philadelphia, was part of the ceremony.
"We did good, right?" he said to Dougherty.
In a brief speech, Kenney highlighted his top priorities, including poverty, universal pre-K, gentrification and quality schools for all neighborhoods.
"Our children shouldn't have to take three buses to attend a good school," he said.
He also touched on neighborhood safety and relations between police and the community.
"Black lives do matter," he said to enthusiastic applause, adding that at the same time, police officers work hard and risk their lives every day.
He said he hopes Philadelphians can work together to make the city fairer for all.
"Government simply cannot do it alone," he said. "We need our businesses, our nonprofits, our universities and everyday Philadelphians to come together and row in the same direction."
Kenney's election is credited, in part, to strong support from the black community - something Irish-American Kenney has said he considers a huge responsibility as he takes office.
He has pledged to create more jobs, including for former felons, in what is the nation's poorest big city.
Kenney assumes office after several years of progress for a city that had endured decades of decline. The murder rate dropped sharply from when Nutter took office, more students are graduating from high school, unemployment is down and Nutter declared that veteran homelessness is "effectively over."
In his time as a city councilman, Kenney worked on inequality, as well as immigration, gay rights and criminal justice reform. Kenney has pointed to his Irish roots and Jesuit upbringing as the influences that make him sensitive to these issues.