LOS ANGELES — A federal judge on Wednesday sentenced the man behind “Innocence of Muslims,” the anti-Islam YouTube video that ignited bloody protests in the Muslim world, to one year in prison for violating parole.

The man, Nakoula Basseley Nakoula, who is also known as Mark Basseley Youssef, a name he legally adopted in 2002, appeared in Federal District Court here and pleaded guilty to four charges of violating a probation sentence imposed on him in 2010 after a bank fraud conviction. Each of his guilty pleas, worked out with prosecutors in advance, was related to his maintenance of the two identities.

In turn, the government agreed to drop four more probation violation charges, all of which pertained to Mr. Nakoula’s work on the “Innocence of Muslims.” Prosecutors had maintained that Mr. Nakoula lied to the police about the extent of his involvement in the project.

In accordance with the sentencing request by Robert Dugdale, the assistant United States attorney who prosecuted the case, Judge Christina A. Snyder ruled that Mr. Nakoula would serve one year in prison followed by four years of probation. She rejected a request for home confinement in lieu of prison from Mr. Nakoula’s lawyer, Steve Seiden, telling Mr. Nakoula that he had already “struck a deal far more favorable than he might have otherwise suffered.”