Reed, 51, was facing death by lethal injection on Wednesday for the 1996 killing of a 19-year-old woman.
Kardashian West revealed she was with Reed when the decision was announced and described the moment he discovered the news on Instagram.
The reality star posted a photograph of Reed in prison, as he placed his hand on a pane of glass that separated the pair.
“Today, I had the honour of meeting #RodneyReed in person and the privilege of sitting with him when he got the news that the highest court in Texas had issued a stay of execution and remanded the case back to the trial court for further consideration,” the caption read.
"Words cannot describe the relief and hope that swept over the room in that moment. That hope had been building over the last few weeks around Rodney's case."
Kardashian West continued by stating how Reed’s case had prompted “people all around the globe speak up” and thanked everyone for their support.
“So grateful for the commitment and passion of everyone who voiced their support, the Texas Board of Pardons and Paroles for their recommendation to issue a 120 day reprieve, and the courts for issuing a stay!”
Kardashian West is currently studying to become a criminal justice lawyer and is planning to take her exams in 2022.
She has become increasingly involved in high-profile cases where supporters of the accused claim there has been a miscarriage of justice.
The mother-of-four played a crucial role in the release of prisoner Alice Marie Johnson, whose life sentence for drug offences was commuted last year.