The fourth test begins on Wednesday at Old Trafford, Anderson's home ground, where England must win to level the series. Australia lead the series 2-1 and even a draw would see them retain the urn.
Anderson, England's leading wicket-taker in tests (688), was rested for the third test after the 40-year-old struggled to make an impact in the series with just three wickets in the first two matches.
Robinson makes way after he was injured in the third test, suffering from back spasms which saw him bowl only 11.2 overs in the first innings. He did not bowl in the second innings with Chris Woakes sharing the new ball with Stuart Broad.
Despite Robinson writing in a Wisden column that he was "100% fit for Manchester", England have gone with Anderson's experience while Mark Wood and Chris Woakes retain their places after they led the hosts to victory in Headingley.
Spinner Moeen Ali is also expected to bat at number three again after he came in one down in the second innings, allowing Harry Brook to come in at number five and play a match-winning knock of 75.
England team: Ben Duckett, Zak Crawley, Moeen Ali, Joe Root, Harry Brook, Ben Stokes (captain), Jonathan Bairstow, Chris Woakes, Mark Wood, Stuart Broad, James Anderson.
