The move sees Jamie Roberts switch from full-back to inside centre with Stephen Jones remaining at fly-half and Sonny Parker dropping out of the 22 altogether.
Roberts scored a try at Vodacom Park on Saturday in a mixed display and will be playing out of position when he lines up in midfield.
In the pack, captain Ryan Jones has been shifted to blindside flanker to accommodate the promotion of Gloucester's Gareth Delve from the bench.
Jonathan Thomas has been asked to take the openside duties vacated by Dafydd Jones, who must settle for a place among the substitutes.
Ospreys hooker Richard Hibbard starts at hooker in place of the injured Matthew Rees, Gethin Jenkins switches to loosehead and Rhys Thomas replaces Adam Jones at tighthead.
In all there are seven changes to the side defeated in the first Test, three positional.
Gatland revealed the pressing need to involve Hook forced his selection at full-back.
"We know what James Hook can do and we believe we need him on the pitch from the start as he is too good a footballer not to be used," he said.
"He has gone well at full-back in training during some pretty intense sessions and he will be able to play a big part in the game from 15.
"Knowing how physical the South African midfield were last week, Jamie is the biggest back we had on the field so he will give us more go forward in the centre position."
Gatland added: "All three back row forwards we have chosen have vast experience in the positions they will play on Saturday.
"We believe it will give us a physical combination capable of improving our performance at the breakdown where we need to improve.
"Some of the combinations in this selection are new but we are very well aware of the capabilities of the boys we have chosen and we know what options they offer us."
Wales team to play South Africa at Loftus Versfeld, Pretoria, on Saturday June 14:
J Hook (Ospreys); M Jones (Llanelli Scarlets), T Shanklin (Cardiff Blues), J Roberts (Cardiff Blues), S Williams (Ospreys); S Jones (Llanelli Scarlets), G Cooper (Gloucester); G Jenkins (Cardiff Blues), R Hibbard (Ospreys), R Thomas (Dragons), I Gough (Ospreys), A-W Jones (Ospreys), R Jones (Ospreys, captain), J Thomas (Ospreys), G Delve (Gloucester).
Replacements: T R Thomas (Cardiff Blues), D Jones (Ospreys), I Evans (Ospreys), D Jones (Llanelli Scarlets), W Fury (London Irish), A Bishop (Ospreys), T James (Cardiff Blues).