Cook made an unbeaten half-century against the tourists for South Africa A in a warm-up match before the series.
The 33-year-old is the son of former Proteas Test batsman Jimmy Cook.
England have already won the four-match series and lead it 2-0 after beating South Africa by seven wickets in Johannesburg on Saturday.
"Stephen has been in excellent form this season and gives us another option at the top of the order," said chief selector Linda Zondi.
He looks set to replace the out-of-form Stiaan van Zyl, who has made just 69 runs in five innings at the top of the order.
Cook has scored two centuries and a 76 in his past three matches for the Highveld Lions.
Dale Steyn retains his place in a 17-man squad for the match, but is thought to be struggling with the shoulder injury that has kept him out of the past two Tests.
Quinton de Kock is also set to return as wicketkeeper. He was ruled out of the third Test after injuring his knee while walking his dogs, but his replacement Dane Vilas has not been included this time.
South Africa squad: AB de Villiers (c), Kyle Abbott, Hashim Amla, Temba Bavuma, Stephen Cook, Quinton de Kock (wkt), JP Duminy, Faf du Plessis, Dean Elgar, Morne Morkel, Chris Morris, Dane Piedt, Kagiso Rabada, Rilee Rossouw, Dale Steyn, Stiaan van Zyl, Hardus Viljoen.
Uncapped opener Stephen Cook has been added to the South Africa squad for the final Test against England, which starts in Pretoria on Friday.