Flanker Kvesic, who made a Test match breakthrough with England in Argentina this summer, moves from his familiar openside position to blindside when Gloucester tackle Aviva Premiership rivals Saracens at Allianz Park on Sunday.
And Savage saw enough from the 21-year-old former Worcester player, even in defeat against Sale Sharks last weekend, to know that Gloucester have landed a significant recruit.
"Matt was a real positive against Sale," Savage said.
"He has fitted in really well from Worcester and has stepped up already, bringing a lot of power and quality beyond his years.
"Looking at him you have to double-take when he says how young he is. He has got a lot of Premiership experience already under his belt, and he added to that with England over the summer.
"Moving forward, he's definitely the kind of player we can build parts of our team around. It's also really helped out with the competition from the back-row. You definitely get the best out of everyone."
Apart from switching roles for Kvesic, Gloucester rugby director Nigel Davies has replaced England number eight Ben Morgan with Sione Kalamafoni and handed Akapusi Qera the number seven shirt, while Wales international scrum-half Tavis Knoyle makes his first Premiership start.
And Davies has challenged his players to "redeem themselves" against Saracens following last Saturday's deflating loss.
"We have made one or two changes. But, in the main, it's up to the guys to redeem themselves, really," Davies said.
"There is some technical stuff that we have to get right in terms of the set-piece. And, when we get more ball, we can actually dictate for longer periods of the game.
"It may not be a huge tactical game on Sunday.
"It may well come down to whoever wants it the most. It's the sort of thing that Saracens pride themselves on, in terms of dominating the opposition and being more physical.
"It is a great challenge, it's exactly what we want. Probably the best fixture we could have had."
Saracens rugby director Mark McCall has made a solitary switch to the side that accounted for London Irish 42-20 seven days ago, with centre Duncan Taylor taking over from England international Brad Barritt and partnering Joel Tomkins in midfield.
"We got off to a winning start against London Irish last weekend, and we were pleased with the result but we know that we can improve on our performance," McCall said.
Last season's play-off loss to Northampton apart, Saracens have suffered just one defeat in their last nine Premiership games - against Gloucester five months ago.
Gloucester, meanwhile, have not opened a league campaign with successive defeats since 2000, but they last triumphed away in the Premiership at Northampton on February 9.