The England U-16 international has accepted an offer of a two-year scholarship at Elland Road starting next summer.
Leeds chief exceutive officer Shaun Harvey said in the Yorkshire Evening Post: "We are delighted at his decision. He was the subject of an offer from Chelsea but we turned that down. We believe that both his and our best long-term footballing interests are best served if his future is with Leeds United."
Academy boss Neil Thompson was also pleased to secure the youngster's signature and is looking forward to working with the midfielder. "Now it is about realising that potential," he said. "He has played for the England Under-16s and he has been in our Under-18 Academy side since Christmas, although he is still only 15.
"He is a left-footed, attacking midfield player, aggressive and good in the tackle. We feel he will be able to develop with us and that is why he decided to stay here."
Rose is one of 10 players to accept a two-year scholarship. The other players joining the Academy next season are:
Nathan Cartman (Hipperholme and Lightcliffe High School, Halifax)
Oliver Hotchkiss (Houghton Keepier HS, Durham)
Ross Wilkinson (Gilesgate Sports College, Durham)
Stefan Connor (Lawnswood HS, Leeds)
Fabian Delph (Tong Secondary School, Bradford)
Christopher Fisher (Morley HS, Leeds)
Duane Grace (Willow Garth HS, Barnsley)
Jason Mycoe (Selby HS)
Chris Ovington (Rodillian HS, Wakefield).