The journalist, 57, opened up after Turnbull passed away at the age of 66, following a battle with prostate cancer.
Williams revealed that the pair met in America in the early 90s when she was a "rookie" and that she collapsed over a meal because of jetlag and nerves.
Turnbull helped her and went on to keep the incident to himself for more than two decades.
She told The Telegraph the pair met in the US during the 1992 presidential election campaign and that she was "nervous" and determined to prove herself.
Williams and Turnbull were going to be working on a programme about Bill Clinton and met at a restaurant to talk about it.
Watch: Former BBC Breakfast Bill Turnbull host dies aged 66
However, during their meal she "keeled over and collapsed".
“He called the paramedics and we spent the first evening of our trip in the hospital’s ER department," she said.
"I was fine - it was probably jetlag and nerves - the trip was memorable, the programme (eventually) was a good one and he vowed never to tell anyone what had happened. He kept that secret for 25 years."
Williams said that when the pair were flying home to the UK, Turnbull joked that he would only work with her again if she didn’t pull another stunt like that.
The pair ended up working together again in 2001 when they were both on BBC Breakfast.
They sat next to each other on the sofa until 2012, when Williams left the programme.
Paying tribute on Twitter after Turnbull passed away, Williams said he was "the kindest, most generous of presenters".
Goodbye, Billy. The kindest, most generous of presenters. A wonderful friend for 30 years. And a man devoted to his family. All thoughts and love with them.
You will be so, so missed - thank you for the laughter and friendship xxhttps://t.co/Jr85ymAehy pic.twitter.com/IfvxrH0BXn
— Dr Sian Williams (@sianwilliams100) September 1, 2022
She went on: "A wonderful friend for 30 years. And a man devoted to his family.
"All thoughts and love with them. You will be so, so missed - thank you for the laughter and friendship xx."