U.S. District Judge Kurt Engelhardt approved the plea deal in New Orleans.
The 72-year-old Durst is still facing a murder charge in Los Angeles for the 2008 slaying of his friend Susan Berman.
A recent HBO documentary about Durst led legal authorities to reopen the case regarding his wife, Kathleen's disappearance.
Kathleen Durst disappeared from the couple's South Salem home after an argument in 1982 and according to New York State Police investigator Joseph C. Becerra, both his division and the Westchester District Attrorney's office are still looking into her disappearance, The New York Times reported.
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