Currie, 18, made his Super League debut against Widnes earlier this year and went on to make five appearances for the first team, and has now been rewarded with a new five-year deal.
Fellow back-rower Laithwaite is signed until November 2015 while centre Saltonstall has signed a new four-year deal.
Saltonstall, who joined the club from amateurs Siddal, was part of Warrington’s triumphant Valvoline Cup team, alongside Currie.
Wolves Head Coach Tony Smith said: “I’m really excited for all three players. James (Laithwaite) has already experienced Super League on loan at Hull KR and Ben’s also had a taste of first grade with us. I expect that James (Saltonstall) won’t be too far behind with the rate he’s progressing. We’re really excited about them not only because of their potential but also their attitude. They’re exciting young players and I‘ve got no doubt that they will go on to be favourites at Warrington in the near future.
“This is all part of our progression as a club; to produce highly talented young players as well as bringing in the occasional player from outside.”