Cueto will miss England's opening World Cup clash with a lower back problem that he aggravated in the warm-up win over Ireland.
And although Cueto could have played in an emergency, Armitage, who is predominately a full-back, gets the nod to come in on the left wing.
"Mark's had a little bit (of back trouble) before but he could have played (against Argentina)," said England boss Martin Johnson.
"There's a grey area between fit and injured in where most players sit all of the time.
"He trained fully all week but he's not quite where he needs to be - but the good things for us is Delon is playing very well.
"It's quite a simple decision. Delon been around for a few years now, we know when he is in form he is a Test match player. We've no qualms about picking him in any of the back three positions."
As expected Nick Easter also comes into the side having recovered from the calf strain that kept him out the side for the final warm-up match.
Easter starts at No.8 with James Haskell moving to openside to replace the injured Lewis Moody.
Mike Tindall will skipper the side in Moody's absence, with Manu Tuilagi, Louis Deacon, Richard Wrigglesworth, Steve Thompson and Jonny Wilkinson all retaining their places.
There is a place for the fit-again Ben Youngs on the bench, with the Leicester scrum-half having been sidelined for three months after a knee operation.
Argentina confirmed their team on Tuesday, making just one change from their warm-up defeat to Wales with Gonzalo Tiesi returning to the centres.
And although the Pumas boast one of the most ferocious packs in the game, Johnson believes their back division can be as equally dangerous.
"They do what they do very well but they've got more dimensions to them than is sometimes made out," said Johnson.
"They are a dangerous running side, they come at you through forwards but put you under pressure with their kicks as well. It's a full-on Test against a team that finished third in the world last time.
"You have to get it right in the moment, right from the opening kick-off."
England: 15 Ben Foden, 14 Chris Ashton, 13 Manu Tuilagi, 12 Mike Tindall (capt), 11 Delon Armitage, 10 Jonny Wilkinson, 9 Richard Wigglesworth, 1 Andrew Sheridan, 2 Steve Thompson, 3 Dan Cole, 4 Louis Deacon, 5 Courtney Lawes, 6 Tom Croft, 7 James Haskell, 8 Nick Easter.Replacements: 16 Dylan Hartley, 17 Matt Stevens, 18 Tom Palmer, 19 Tom Wood, 20 Ben Youngs, 21 Toby Flood, 22 Matt Banahan
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