New York state Assembly Speaker Sheldon Silver was accused by federal prosecutors on Thursday of using his political power to amass a “tremendous personal fortune” through kickbacks from real-estate developers and referrals to a personal-injury law firm.

Manhattan U.S. Attorney Preet Bharara issued a sweeping condemnation of Mr. Silver, a Manhattan Democrat and one of the most powerful state lawmakers, just hours after the speaker surrendered to the Federal Bureau of Investigation to face corruption charges following a long-term...