New York City's economic-development agency and two related organizations admitted in a settlement Monday that they illegally lobbied the City Council on behalf of projects at the heart of Mayor Michael Bloomberg's redevelopment agenda.

The concessions came after a three-year probe by the state attorney general's office. Investigators found that the Economic Development Corp. worked behind the scenes with the groups—called local development corporations—to nudge lawmakers to support projects in Willets Point in Queens and...