Anderson, 35, who has 506 Test wickets, was promoted as understudy to captain Joe Root ahead of fellow paceman Stuart Broad and ex-skipper Alastair Cook.
Coach Trevor Bayliss previously said he was planning for an Ashes series without Stokes, who is running out of time ahead of the first Test in Brisbane from November 23.
Stokes remains at home awaiting the outcome of a police probe into his involvement in the brawl outside a Bristol nightclub on September 25.
Nottinghamshire speedster Jake Ball is to have a scan after he injured his right ankle on Thursday during England's warm-up game against a Cricket Australia XI in Adelaide.
It follows a knee injury which ruled paceman Steven Finn out of the tour.
Surrey all-rounder Tom Curran has arrived as Finn's tour replacement, while all-rounder Moeen Ali continues to recover from a side strain.