Williams has been ruled out of the tournament after suffering an ankle injury in training.

Centres Davies and Hadleigh Parkes have been named in the side despite battling with injuries.

Injured back-rower Josh Navidi is replaced by Ross Moriarty.

There are three changes from the side that started against France, with Davies replacing Owen Watkin.

Halfpenny, 30, has only made one start in the tournament so far - a man-of-the-match performance against Uruguay.

Head coach Warren Gatland says the loss of Williams is a big blow but believes Halfpenny will add different qualities and hinted both players might have started had Williams been fit.

"Liam is undoubtedly a big loss from an attacking perspective and what he has achieved in the game in the last year or so," said Gatland. "But bringing in the experience of someone like Leigh gives us a different element.

"He is defensively probably the best full-back in the world in terms of his aerial game and coverage defensively.

"We had a long debate about whether we started Leigh in the first place and potentially move Liam to the wing.

"There was a long discussion about that, so Leigh was probably unlucky he was not in the team in the first place."

Gatland confirmed Dan Biggar would retain the main goal-kicking duties, with Halfpenny lined up to take the longer kicks.

Davies had initially been named in the team against France for the quarter-final but was a late withdrawal after failing to recover from the knee injury he suffered against Fiji in the pool stage.

The Scarlets centre has again been training this week with his left leg heavily strapped.

"We hope he is fit - he has come through training this week," said Gatland.

"He was very close last week and he made a decision to rule himself out for the betterment of the team."

Centre Parkes has started all five games in Japan so far but picked up a small broken bone in his hand in the opening match against Georgia and sustained a shoulder problem against Uruguay.

With Moriarty being promoted to the starting side at number eight, Scarlets back-rower Aaron Shingler comes in on the replacements bench, where he is joined by Watkin.

Scrum-half Gareth Davies will win his 50th cap against the Springboks in Yokohama.

Wales: Halfpenny; North, J Davies, Parkes, Adams; Biggar, G Davies; Wyn Jones, Owens, Francis, Ball, Alun Wyn Jones (capt), Wainwright, Moriarty, Tipuric.

Replacements: Dee, R Carre, D Lewis, Beard, Shingler, T Williams, Patchell, Watkin.

South Africa: Le Roux; Nkosi, Am, De Allende, Mapimpi; Pollard, De Klerk; Mtawarira, Mbonambi, Malherbe, Etzebeth, De Jager, Kolisi (capt), Du Toit, Vermeulen.

Replacements: Marx, Kitschoff, Koch, Snyman, Mostert, Louw, H Jantjies, Steyn.