Durst will serve 7 years and one month in prison on the charge that's kept him in Louisiana pending a murder trial in California.
Judge Kurt Engelhardt approved the sentence which Durst, 72, accepted as part of his guilty plea in February.
VIDEO: Robert Durst to enter plea on gun charge
Ten years and a $250,000 fine would be the maximum sentence for illegally carrying a .38-caliber revolver after being convicted of a felony.
Durst is charged in Los Angeles with killing his friend Susan Berman in 2000 to keep her from talking to New York prosecutors about the disappearance of Durst's first wife in 1982.
His attorneys have said repeatedly that he's innocent, doesn't know who killed Berman, and wants to prove it.
VIDEO: Robert Durst pleads guilty to weapons charge
The most recent such statement was in a motion filed Monday asking U.S. District Judge Kurt Engelhardt to recommend that Durst serve his time at Terminal Island, California, about 30 miles from downtown Los Angeles, because it's near where Durst faces trial and it has medical facilities Durst needs because of his "advanced age and serious health considerations, including mobility challenges."
An estranged member of the wealthy New York real estate family that runs 1 World Trade Center, Durst was tracked to New Orleans in March 2015 by FBI agents worried that he was about to flee to Cuba.
He was detained at a hotel on the eve of the finale of a six-part documentary about him, and was arrested early on the morning of the show. "The Jinx" described the disappearance of Kathleen Durst, the death and dismemberment of a neighbor in Galveston, Texas, and Berman's death.
At the end of the show, Durst is heard muttering, "What the hell did I do? Killed them all, of course."