Williams, who is currently helping boost Uganda's hopes of qualifying for next year's World Cup, will start his new position on October 1.
Chief executive Nico Swartz revealed the Pumas went through a lengthy selection process before making their decision, with Williams beating off competition from former Springboks Ian Macdonald and Hugh Reece-Edwards.
"The presentation Chester made to the directors was very impressive and he, in turn, accepted the offer we made to him," said Swartz.
Williams, nicknamed the "black pearl" during the historic 1995 tournament, took over as Springbok Sevens coach and has enjoyed much success, including a win in Dubai in 2004, before being named as the coach of the Cats in 2005. He was fired the same year after losing 11 out of 12 games.
He was then appointed South Africa A coach, but has never coached the team as they have not played a fixture in the last two years.