The squad will be co-captained by hooker Dewi Lake (24) and back row Jac Morgan (23), with centre George North (31) to appear at his fourth World Cup, an experienced player in what is otherwise a largely youthful selection.
Scrum half Gareth Davies (33), prop Tomas Francis (31), blindside flanker Dan Lydiate (35) and full backs Leigh Halfpenny (34) and Liam Williams (32) will all compete in their third World Cup.
Anscombe and Faletau have not played in any of Wales’ warm-up games due to injury but have been deemed too important to leave at home.
Anscombe is one of three fly halfs in the squad along with Dan Biggar (33) and Sam Costelow (22).
Cuthbert was due to line up against South Africa on Saturday but was a late withdrawal due to injury, having recently been plagued by knocks.
Instead Josh Adams (28), Rio Dyer (23) and Louis Rees-Zammit (22) are the wings selected for the tournament in France.
Gatland has gone for a 19-14 split between forwards and backs, having whittled his original squad down from 48 to the required 33.
"The toughest part of the job is always selection and this is particularly the case when it comes to picking a Rugby World Cup squad," Gatland said.
"Over the past three months the whole group of 48 players in the wider training squad has been outstanding in terms of attitude and effort, so having to reduce the squad down to the final 33 has been really hard and there have been some close final decisions in the last 36 hours.
"We have a few more training sessions here in Wales before we depart for France on September 3rd and we cannot wait to get out there and get started in this tournament. We look forward to what lies ahead for this group."
Wales open their World Cup campaign against Fiji in Bordeaux on September 10th, and also have Portugal, Australia and Georgia in their pool.
Wales World Cup squad
Forwards: Taine Basham, Adam Beard, Elliot Dee, Corey Domachowski, Ryan Elias, Taulupe Faletau, Tomos Francis, Dafydd Jenkins, Dewi Lake (co-captain), Dillon Lewis, Dan Lydiate, Jac Morgan (co-captain), Tommy Reffell, Will Rowlands, Nicky Smith, Gareth Thomas, Henry Thomas, Chris Tshiunza, Aaron Wainwright
Backs: Josh Adams, Gareth Anscombe, Dan Biggar, Sam Costelow, Gareth Davies, Rio Dyer, Mason Grady, Leigh Halfpenny, George North, Louis Rees-Zammit, Nick Tomkins, Johnny Williams, Liam Williams, Tomas Williams