Head coach Sir Clive Woodward had been heartily impressed with Thomas' leadership of the Wales team during the autumn internationals and the RBS 6 Nations.
He views the 31-year-old as crucial to the Lions' chances of winning the last two Tests and pulling off a series victory.
Woodward said: "Gareth Thomas is an outstanding player and a natural leader. We are going to need big characters out there who can dig deep and show real fight and courage.
"Gareth is such a character. We did not play as well as we could or should have but I am in no doubt we can beat New Zealand.
"Gareth's leadership will be central to meeting that challenge."
Thomas was mentioned as a potential Lions captain by Woodward last winter after he had spent a week in the Wales camp.
"It is an unbelievable honour for me to be named captain for the rest of the tour," Thomas said.
"It is not the circumstances I would have liked but we are professional rugby players and I am sure Brian wants us to go out there and give it all we can.
"We can't dwell on it now as far as I am concerned. And the New Zealanders better understand I will be around a lot longer than a couple of minutes.
"This is a squad of great players with a lot of fight in them and we are going to put disappointment behind us and show the world what we are made of."
The Lions discovered late on Saturday night that Keven Mealamu and All Blacks captain Tana Umaga had escaped any punishment for the "double spear-tackle" which left O'Driscoll with a dislocation so severe it took medics half an hour to put his shoulder back in.
The Lions management lodged a complaint with the independent citing commissioner, Willem Venter but the South African decided the matter should go no further.
O'Driscoll nevertheless felt the tackle - in which he was lifted off the ground and then dropped head first to the deck - was "deliberate foul play".
He said: "It was a cheap shot which has put me out of the tour. The truth is it could have been an awful lot worse because they could have quite easily broken my neck."
Thomas admitted his players will be fired up for retribution in Wellington next Saturday but insisted it will be of the rugby variety.
"It is not an excuse to go out and get revenge. For me, getting revenge would be winning on Saturday," Thomas added.
"The fact that he was put out of the game in the way that he was will fire every single one of us to get out there and do better in the second and third Tests.
"It is a disappointing incident and myself and the rest of boys are terribly upset for Brian. He is a quality person on and off the field and he was a guy we were all willing to follow.
"I am now captain but in my eyes Brian is still the captain of the 2005 Lions. He is going to stay with us and still play a big part in this trip.
"Brian would be the first to say we have to get over the disappointment of losing him in those circumstances and get on with the job of preparing for Tuesday's match [against Manawatu] and then the second Test."