Former New York State Assemblywoman Pamela Harris pleaded guilty to fraud charges Tuesday, admitting she pocketed city and federal funding intended for vulnerable children and superstorm Sandy victims.

Ms. Harris, a Democrat, was indicted in January and accused of defrauding government agencies out of tens of thousands of dollars from November 2012 through January 2017. Prosecutors said this included falsely telling the Federal Emergency Management Agency that she had been forced out of her home after the storm and collecting...