Reed, 51, is on death row after being convicted in the 1996 killing of 19-year-old Stacey Stites in Bastrop. Prosecutors said Stites was raped and strangled.
Reed has maintained his innocence.
Lawmakers from both parties and celebrities have asked the government to stop Reed's planned execution. On Friday, the Texas parole board recommended a 120-day delay in Reed's execution and moments later the stay was handed down by the appeals court.
"Words cannot describe the relief and hope that swept over the room in that moment," Kardashian said in an Instagram post about her visit with Reed. "That hope had been building over the last few weeks around Rodney's case."
A post shared by Kim Kardashian West (@kimkardashian) on Nov 15, 2019 at 4:21pm PST
Since Texas resumed executions in 1982, only three death row inmates have had their sentences commuted to life in prison within days of their scheduled executions.
The Associated Press contributed to this story.
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