“This was horrible news to wake up to this morning,” said Rassie Erasmus, director of rugby.
“There was a very sombre mood in the breakfast room, it really is unbelievable news.”
Williams died from a heart attack in Cape Town on Friday. He was 49.
“I played with Chester and many of our management knew him well and we are all in shock this morning.
"Many of our players were too young to remember the 1995 Rugby World Cup final, but they have grown up watching highlights of the final and of Chester and know him as a rugby player who became an icon for our country.
“Only this week our management team was chatting to Chester about his plans to come to the tournament and about tickets for Rugby World Cup matches. It will take us some time to get over this shock.
“Our thoughts and prayers right now are particularly with the family that Chester has left behind, with Maria and the children. We have lost a legend, they have lost a husband and father.
“It’s probably no comfort to them now, but I am sure that Chester’s name will go down with the greats of South African rugby as a player and for what he stood for in our country’s history.
“This is a very sad day for South Africa and South African rugby.”
The Springboks were travelling from Kumagaya to a new training base in Kagashima on Saturday.