The 18-year-olds, who are both wingers, are now tied to the Carrow Road club until the summer of 2017 after they were rewarded for their success in 2013.
The pair were both part of the Norwich side that lifted the FA Youth Cup this year, while Josh has already made seven first-team appearances as a substitute this season.
Norwich manager Chris Hughton told the club's official website: "I'm probably as excited about this as I was about any of the signings we've made in the summer or during the season because they're two lads who came through the Academy system.
"They've been very good teenagers here at the club and they've developed very well. When you're able to reward that, it's something very exciting for the future.
"I know it's news for which the response of the supporters will be very good. They've deserved it on what they've done so far, and now the next stage for them is to try and keep that development going."
Josh Murphy, who scored on his debut in the Capital One Cup tie against Watford in September, said: "I do everything with Jacob, we've got a close bond so for both of us to sign long contracts with the club is great."
Jacob Murphy, who has yet to feature for the first team, added: "It's the perfect Christmas present. I'm happy for Josh and for myself as well to get some personal recognition. I'm delighted to sign a new contract."