The 20-year-old, a product of the Oakwell academy, will remain with the Reds until the summer of 2016.
"Danny is one of a number of younger players the club feel have very good potential," manager Danny Wilson told the club's official website.
"The games I've watched him in over recent weeks, he's been very impressive.
"From my point of view, there's nothing better than seeing one of your own coming through and it's testament to everybody in the academy for their hard work, so let's hope there's more to come."
Rose, who made his first-team debut as a 17-year-old in 2011, has made a total of 15 appearances, mainly off the substitutes' bench and has scored two goals.
Rose said: "I'm pleased and proud to extend my stay at the club I love.
"I'm determined to get a shirt in the starting XI as there's no better feeling than pulling on that red shirt and sticking the ball in the net.
"The hard work continues and I'm just looking to improve myself as a player and person over the next two and a half years and beyond.
"Once again I'd like to thank everyone in the academy, all of my friends and family for their support."
- Sports & Recreation