"She's very disciplined. Of course she's a kid at heart, but when it comes to her schedule, what she eats, how she sleeps... her dad does not have to beg her to come to practice.
"It's how I've watched her develop over the years because this is her dream. It wasn't her dad's dream or her mum's dream, she's worked hard to obtain it and I cannot express how proud I am."
Gauff acknowledged after her third-round win against Slovenia's Polona Hercog that she had witnessed her teenage life change "in a matter of seconds".
She could not hide her delight that Tina Knowles, mother of Beyoncé, the pop star, had sent her a congratulatory message via Instagram, while her shock when she defeated her idol Venus Williams on day one of the tournament was plain to see.
Messages of congratulation have poured in from all over the world, with Michelle Obama, the former First Lady, Miranda Hart, the British comedian, Reese Witherspoon and Samuel L Jackson, the Hollywood actors, all heaping plaudits on the schoolgirl.
But Mrs Odom said she was confident that her granddaughter's drive was strong enough not to be swayed by the hype.
"Her dad tells the story of how [when she was very young] she could focus for 15 minutes without getting distracted, so he knew that [tennis] would probably be a good sport," she told BBC Radio 5 Live.
"She wanted to win a grand slam and be the greatest of all and she has worked, she has really worked at it.
"I hope it will be the same Cori [who comes home]. It's just the atmosphere around her will probably change. This is going to open up doors for kids all around that if you work hard you can obtain your dream.
"Then it was [her mum and dad's] responsibility and duty to make sure their child obtained her dream."
For now, Gauff's feet remain firmly planted on the ground. She was so excited about a new album by Jaden Smith, her favourite rapper, on Friday evening that she was keen to speak about that before her stunning Centre Court victory.
When informed she had won a minimum of £174,000 (NZ$328,000), Gauff said she would be spending it on hoodies. "My mum, she bans me from buying hoodies for two months," she said.
"Every week I was getting new hoodies sent to the house. I don't know, I like wearing them because at home you can't wear them because it's so hot.
"I try to wear them as much as possible on the road."
And on her mother's jubilation when she fought back from the brink of defeat to win her last match, she said: "Please tell me she's a meme. She's going to go viral.
"I'm going to retweet it and everything. I'm so excited."
