Jones will partner Ospreys colleague Adam Beard in the second row, while James Davies comes into the back row in place of Aaron Wainwright.
Up front there are two new props as Nicky Smith and Dillon Lewis get the nod either side of Ken Owens.
Jonathan Davies and Josh Adams are the only members of the backline who remain from the 19-16 semi-final loss to South Africa, with Tomos Williams and Rhys Patchell forming a new-look half-back partnership.
Owen Watkin joins Jonathan Davies in the centres, while Owen Lane replaces the injured George North on the wing and Hallam Amos slots in at full-back.
Wales will look to equal their best-ever World Cup performance of third, achieved back in 1987.
They face a New Zealand team that is the only side that Gatland has not beaten in his time as Wales coach, although he of course did so while in charge of The British & Irish Lions in the 1-1 drawn series in 2017.
Wales’ line-up for the Bronze Final at #RWCTokyo Naw newid am y gêm olaf y prif hyfforddwr.#NZLvWAL pic.twitter.com/mR3Tp1kL8J
— Welsh Rugby Union 🏉 (@WelshRugbyUnion) October 30, 2019
Wales team to face New Zealand:
15. Hallam Amos (Cardiff Blues)
14. Owen Lane (Cardiff Blues)
13. Jonathan Davies (Scarlets)
12. Owen Watkin (Ospreys)
11. Josh Adams (Cardiff Blues)
10. Rhys Patchell (Scarlets)
9. Tomos Williams (Cardiff Blues)
1. Nicky Smith (Ospreys)
2. Ken Owens (Scarlets)
3. Dillon Lewis (Cardiff Blues)
4. Adam Beard (Ospreys)
5. Alun Wyn Jones (Ospreys) (c)
6. Justin Tipuric (Ospreys)
7. James Davies (Scarlets)
8. Ross Moriarty (Dragons)
16. Elliot Dee (Dragons)
17. Rhys Carre (Saracens)
18. Wyn Jones (Scarlets)
19. Jake Ball (Scarlets)
20. Aaron Shingler (Scarlets)
21. Gareth Davies (Scarlets)
22. Dan Biggar (Northampton Saints)
23. Hadleigh Parkes (Scarlets)