Durst died in a state prison hospital facility in Stockton, his attorney Chip Lewis said.
He said it was from natural causes due to a number of health issues.
Durst was convicted in September of shooting Susan Berman at point-blank range in 2000 at her Los Angeles home.
He was sentenced to life on October 14 last year.
Two days later, he was hospitalised with COVID-19, his trial attorney Dick DeGuerin said.