The XI was confirmed shortly before England's captain Ben Stokes addressed the media at Headingley, where his team must win to begin to claw back their 2-0 deficit after defeats at Edgbaston and Lord's.
Of the three changes, Anderson's was the most anticipated. He has so far claimed three wickets at 75.33 in an off-colour start to his tenth Ashes campaign, and after declaring the Edgbaston pitch to be "kryptonite", England's short-ball approach at Lord's also went away from his preferred swing-bowling methods.
"We're obviously devastated for Popey," Stokes said. "He's been a huge part of what we've managed to achieve over the last 18 months and obviously, being vice captain, it's a real shame not only for us, but also for him in such a big series."
Moeen's return provides more ballast in the lower-middle order, and is further reason why England have opted not to replace Pope with an additional batter, with Essex's Dan Lawrence the one spare option in their squad. Harry Brook has been handed Pope's role at No.3, in a show of faith in spite of his quiet series to date, but Stokes admitted that his own workload as an allrounder - after a gruelling 12-over spell in the second innings at Lord's - had been a key reason for packing the side with extra bowling options.
"Obviously Dan was in the squad as the next batter in, but there were a few more things to consider," Stokes said. "I'm not gonna lie, last week took it out of me a little bit, so a big part of it was what would be the best team if I wasn't to bowl a ball in this game, in the worst case scenario? That doesn't mean I'm not going to bowl, but that was a huge part of the thinking about the team that we picked."
Brook has so far made 132 runs at 33 in four innings of the series, but attracted criticism for a soft dismissal at Lord's after reaching his half-century. Stokes, however, said that his promotion to 3 - and Bairstow's to No.5, the position he filled in his remarkable run of form in 2022 - had been "pretty simple" decisions.
"Last summer, Brookie was in the squad and was the next player in, and when you've got a player like Brookie, from one to six, he would have come in in any position," Stokes said. "We feel that Brookie is a type of player who will just take the responsibility and just crack on with it.
"We obviously want to keep Joe [Root] at four because he's a remarkable player, and Jonny moving up to five was just to get him into the game earlier. The things he did last summer from the No.5 position are quite hard to look past."
Moeen missed the Lord's Test after sustaining a cut to the knuckle of his spinning finger, but he has been deemed fit to resume his comeback to the format. His appearance in the first Test at Edgbaston was his first since retiring at the end of the India series in 2021, and he resumes needing two more wickets to reach 200 in Tests.
Wood's extra pace offers England a genuine point of difference after being noticeably out-matched on the speed gun in the first two Tests. After missing the Lord's Test to ensure his readiness for action, he returns for his first Test since the tour of Pakistan in December, and his first competitive outing in all cricket since his fiery displays for Lucknow Super Giants in the IPL in April.
He steps in for Josh Tongue, who produced a spirited display in his first taste of Ashes cricket at Lord's, where he finished with five wickets in the match, including Steve Smith and David Warner in both innings.
Stokes, however, was adamant that Wood's inclusion ahead of Anderson did not spell the end of the road for England's greatest fast bowler, a point that he had made to the whole bowling group before the start of the series.
"We were very open and honest, and clear with each other before the series started, that it's going to be very tough ask to ask all the bowlers to play every game this summer," Stokes said. "It's a good chance for Jimmy to have a rest up and then get ready to charge in from the Jimmy Anderson End at Old Trafford next week. But it's great to have Woody fit. He's firing and really ready to go this week, and we're looking forward to seeing him get going."
England: 1 Zak Crawley, 2 Ben Duckett, 3 Harry Brook, 4 Joe Root, 5 Jonny Bairstow (wk), 6 Ben Stokes (capt), 7 Moeen Ali, 8 Chris Woakes, 9 Ollie Robinson, 10 Stuart Broad, 11 Mark Wood
Andrew Miller is UK editor of ESPNcricinfo. @miller_cricket