The reality TV star spoke of the moment she told great-grandmother Alice Marie Johnson she was being released.
Kardashian West championed Ms Johnson’s case, and even met with US President Donald Trump to discuss her release.
Ms Johnson, 63, was jailed for life without parole for non-violent drug offences in 1997.
She was released earlier this month after Mr Trump commuted her sentence following Kardashian West’s intervention.
In an interview with NBC’s Today, Kardashian West, 37, said she broke down when she told Ms Johnson the news.
“At first I thought she knew because the news was starting to break and we had to get her on the phone,” she said.
“She was kind of quiet on the phone and I know her personality enough to know that she would have been screaming, or something.
“And I said, ‘wait, you don’t know?’ and she said, ‘know what?’ and I was like, ‘you are going home’. And screams, and cries and we all just cried on the phone.”
The two met for the first time on Wednesday and before sitting down for the interview.
Kardashian West told the programme: “I mean, I think to some people it might seem like, ‘okay, Kim made a phone call to the president, showed up’. We had been in talks and working on this for seven months. And it wasn’t an instant thing. It was a lot of work.”
Ms Johnson admitted she had no idea who Kardashian West was when she first learned the star had started championing her cause.
“As soon as I found out who she was, I started getting every magazine I could find… I started reading everything that I could about her. And everyone was amazed. And I was amazed, too.”
Ms Johnson was convicted in 1996 for her part in a cocaine trafficking operation involving more than a dozen people.
She was sentenced to life in prison in 1997.
The president says he is considering a long list of other clemency actions, including for former Illinois governor Rod Blagojevich, who is serving 14 years in prison for corruption, and celebrity homemaker Martha Stewart, who served about five months for insider financial trading.