The 20-year-old's current deal was set to expire and supporters feared the England Under-19 international, their top scorer last season, could walk away from Fratton Park this summer.
Boss Andy Awford told the club's official website: "Signing a three-year deal is important because it shows that Jed is committed to this club.
"He's put down roots here and wants to achieve things with Pompey - we're delighted about that.
"My personal relationship with him has helped, but Mark Catlin and Tony Brown, as well as Jed's agent David Bromley, have all worked hard to get the deal done.
"It's a big season for Jed, but his attributes are there for everyone to see and I'm looking forward to working with him again next season."