The Tonga international was a try-scorer in the Aviva Premiership semi-final and final in 2012/13 and man-of-the-match in the LV= Cup Final win. Mafi was also named Tigers Players' Player of the Year and the Supporters' Young Player of the Year.
Salvi, a former Australia 'A' cap, made his Tigers debut on the opening day of the 2011/12 season and has scored eight tries in 41 appearances as an openside flanker.
Leicester Tigers director of rugby Richard Cockerill said: "Steve and Julian have become key members of our squad and firmly established themselves among the outstanding performers in the Aviva Premiership. I'm delighted that they have agreed to stay and that they feel this is the best place to play their rugby.
"Steve is just 23 years of age and we believe he will get better and better in this environment, playing alongside other top-class players.
"Julian Salvi is an important player for us as an out-and-out openside. He's just 27 but he's an experienced player and has been in very good form with us."
Mafi and Salvi join England international duo Tom and Ben Youngs and Tigers second-row Graham Kitchener in agreeing terms to contracts beyond the end of the current season.