A number of clubs, including Wolverhampton Wanderers and Blackburn Rovers, had reportedly been eager to snap up the 23-year-old.
However, following talks with Leeds manager Brian McDermott, Murphy has decided to pen a three-year contract at Elland Road.
"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. Luke certainly fits the profile of player that we're looking to attract.
"He is young, hungry, wants to work hard and very obviously talented. I'd like to thank the owners for making this deal happen. We had spoken about Luke earlier in the summer being one for the key signings we're looking to make."
Murphy scored 25 goals in his 186 outings for Crewe.