LOS ANGELES—Federal prosecutors charged Michael Avenatti with embezzling millions of dollars in client funds, concealing assets from a bankruptcy court and failing to pay taxes, in the latest criminal troubles for the once high-flying celebrity attorney.

The 36-count grand jury indictment announced Thursday builds on wire-fraud and tax-fraud charges brought last month by U.S. Attorney Nicola Hanna in Los Angeles. That same day, Mr. Avenatti was arrested in Manhattan and charged with attempting to extort more than $20 million...