Jones, who has 70 caps for his country, started both the first and second Tests against the Wallabies and has played a total of six times so far on tour. He featured in all three Tests in South Africa four years ago and will be the only player to match that feat this time around.
Loosehead prop Alex Corbisiero and inside centre Jamie Roberts have both been passed fit to start following their own injury worries, with Corbisiero having missed the second Test with a calf problem. A hamstring injury has prevented Roberts from playing any part in the series so far.
Scrum half Mike Phillips has recovered from a knee injury to reclaim his place in the side, while Ireland's Sean O'Brien replaces Warburton at openside flanker.
Richard Hibbard starts at hooker and Toby Faletau is named at number 8 to take the total number of Welshmen in the side to 10.
Mako Vunipola, Tom Youngs, Jamie Heaslip, Ben Youngs and Brian O'Driscoll are the players to make way, with Vunipola and Youngs senior dropping to the replacements bench but Heaslip, Youngs junior and O'Driscoll miss out altogether.
There are further changes among the replacements as Justin Tipuric steps into the squad following O'Brien's promotion, Richie Gray comes in for Tom Croft and Manu Tuilagi takes over from Alex Cuthbert. Ryan Grant misses out on the matchday 23 in favour of Vunipola.
Speaking ahead of the Sydney showdown, Gatland said: "It all comes down to Saturday. Winner takes all. We know we can leave nothing in the tank and that only a complete performance will get us across the line.
"Picking this team was not easy and ultimately with several players available after recovering from injury the head overruled the heart in many selection decisions.
"It has been a challenging tour and we have had our fair share of injuries but we always knew that would be the case. Brian O'Driscoll is a great player and has had a wonderful career but for the final Test in Sydney we just felt Jamie Roberts' presence offered us something more.
"Mike Phillips and Alex Corbisiero were first Test selections and would probably have played in the second Test if not for injury. Richard Hibbard, Toby Faletau and Sean O'Brien have also earned their starting places."
Tweeting about missing out on selection, O'Driscoll said: "Obviously totally gutted at being left out for deciding Test, but all efforts go into preparing the boys to see it through."
Tour manager Andy Irvine admits that everything points towards a fantastic finale in Sydney, with a capacity crowd set to witness what he believes will be another nail-biting encounter between two evenly-matched teams.
"It has been a great tour on and off the field. The hospitality we have received from the Australian people has been outstanding. The banter between the fans has been in great spirit and to date we have had two incredibly exciting Tests," added Irvine.
"It is amazing that the last three series between the Lions and the Wallabies have gone down to the last Test. In 1989 the Lions triumphed, in 2001 it was the Wallabies who won the series, and now in 2013 we go to ANZ Stadium in Sydney with the series and the Tom Richards trophy up for grabs.
"There is nothing between these two teams, with the last two Tests being decided in the dying moments. The Test is a sell-out and the whole rugby world is looking forward to the match with great anticipation."
BRITISH & IRISH LIONS Team & Replacements (v Australia, 2013 British & Irish Lions Tour Third Test, ANZ Stadium, Sydney, Saturday, July 6, kick-off 8.05pm local time/11.05am Irish time):
15. Leigh Halfpenny (Cardiff Blues/Wales)
14. Tommy Bowe (Ulster/Ireland)
13. Jonathan Davies (Scarlets/Wales)
12. Jamie Roberts (Cardiff Blues/Wales)
11. George North (Scarlets/Wales)
10. Jonathan Sexton (Leinster/Ireland)
9. Mike Phillips (Bayonne/Wales)
1. Alex Corbisiero (London Irish/England)
2. Richard Hibbard (Ospreys/Wales)
3. Adam Jones (Ospreys/Wales)
4. Alun Wyn Jones (Ospreys/Wales) (capt)
5. Geoff Parling (Leicester Tigers/England)
6. Dan Lydiate (Newport Gwent Dragons/Wales)
7. Sean O'Brien (Leinster/Ireland)
8. Toby Faletau (Newport Gwent Dragons/Wales)
16. Tom Youngs (Leicester Tigers/England)
17. Mako Vunipola (Saracens/England)
18. Dan Cole (Leicester Tigers/England)
19. Richie Gray (Scotland)
20. Justin Tipuric (Ospreys/Wales)
21. Conor Murray (Munster/Ireland)
22. Owen Farrell (Saracens/England)
23. Manu Tuilagi (Leicester Tigers/England)