The 23-year-old has signed a three-year deal at Elland Road to become the club's second signing of the summer after Oldham striker Matt Smith.
Murphy came through the ranks of the famous Crewe Academy and made his debut as a teenager, and by the end of last season he had become a regular in midfield and had been named captain.
He was the subject of interest from Wolves and Blackburn among others, but Brian McDermott was able to tempt him to West Yorkshire and is excited by his addition to the squad.
"Myself, the owners, the staff, the players, and I'm sure and I can speak for the supporters on this one, are absolutely delighted to sign Luke," McDermott
told the club's official website.
"He's a player I've known for a long time, I've watched his career progress, and I feel he was the best player in his division last year.
"I'd like to thank the owners for making this deal happen. We had spoken about Luke earlier in the summer being one of the key signings we're looking to make."