Carney and Lt. Gov. Bethany Hall-Long, also a Democrat, took their oaths of office Tuesday morning in a rain-soaked ceremony on the steps of Legislative Hall.
Carney acknowledged the state's challenges, including significant state budget problems and unabated gun violence in Wilmington, the state's largest city, but said they can be met with hard work and cooperation among state and local officials.
Carney was elected governor eight years after losing a hard-fought Democratic primary to Gov. Jack Markell.
He went on to serve as Delaware's lone representative in the U.S. House in 2010.