Edmondson, 16, has put pen to paper on a two-and-a-half year deal with the Championship giants.
He will initially link up with Leeds’ Under-18s and Under-23s.
Leeds claim to have seen off competition from ‘opposition rivals’ for Edmondson, who supports the club.
“When [York manager] Martin Gray gave me the opportunity to make my first team debut last month it was a massive step in my career,” Edmondson said.
“It’s a big step now to move from York to Leeds but I have been a Leeds fan ever since I was a kid and it’s always been my dream to play at Elland Road.
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“It is a difficult decision to leave York because I have only just started my scholarship and there is an amazing group of lads in the youth team.
“I have enjoyed every single second of my time at York and it’s a very friendly environment for a young player.
“Moving to any other club was going to be hard but I am going to my ‘dream’ club.
“I never expected to move from York to a Championship club but my aim is to push myself as hard as I can.
“I am still pinching myself now and worry that I might wake up from this dream! It’s all very surreal.”
Edmondson, who was picked up by York after being released by Huddersfield, became the third-youngest player in City’s history when he made his National League North debut last month.
“I have really enjoyed my time at York City and I am grateful for the opportunity the club has given me,” he said.
“When I first arrived, I was not that confident as a player because I had been knocked back by Huddersfield. But the coaching staff here picked me up and gave me the confidence to play my game as I do now.
“I have progressed a lot since coming to the club. Steve Torpey has been a massive influence and the academy staff have pushed me to push myself and strengthened my desire.”