England dropped Zak Crawley to add an extra bowler due to concerns around Ben Stokes’ fitness with the all-rounder having struggled with a quadriceps injury. Sam Curran was also left out.
Archer had been suspended for the second test after breaking biosecure protocols and he spoke earlier this week of his mental anguish after being racially abused on social media while spending five days in quarantine.
Yet after showing lightening pace in the nets in the build-up to the test, he has been selected along with veteran Anderson and Stuart Broad, who resume their long-standing partnership.
Broad, 34, remains in the side after taking six wickets in England’s 113-run victory over the West Indies in the second test and Anderson returns after being rested. The 37-year-old is just 13 wickets shy of reaching 600 test wickets.
Chris Woakes is the other bowler as England sacrificed a batsman.
The West Indies made just one change with Rahkeem Cornwall adding a frontline spinner in place of Alzarri Joseph.
West Indies captain Jason Holder said he had selected to bowl because of the wet conditions.
“I think there is enough moisture in the surface for us to try to make sure of it,” he said.
England – Rory Burns, Dom Sibley, Joe Root (capt), Ben Stokes, Ollie Pope, Jos Buttler (wkt), Chris Woakes, Dom Bess, Jofra Archer, Stuart Broad, James Anderson.
West Indies - Kraigg Brathwaite, John Campbell, Shai Hope, Shamarh Brooks, Roston Chase, Jermaine Blackwood, Shane Dowrich (wkt), Jason Holder (capt), Rahkeem Cornwall, Kemar Roach, Shannon Gabriel. (Writing by Mark Gleeson in Cape Town; Editing by Toby Davis)