Murphy made the switch to the Championship outfit on Monday for a fee reported to be in the region of £1million, penning a three-year deal at Elland Road having previously also held talks with Wolves and Blackburn.
The 23-year-old midfielder rose through the Academy ranks at Gresty Road, making his debut in December 2008, before going on to make 186 appearances for the Alex over five seasons, scoring 25 goals.
Murphy is the latest in a long list of talented players to have produced by Crewe and stresses he will never forget the time spent at his local club.
"I can't speak highly enough of Crewe and what they have done for me. There are people there past and present who made me into what I am today and I can't thank them enough," Murphy told the club's official website.
"They have nurtured into me being here. The amount of players Crewe produce isn't a fluke and that is great credit to the coaches who are there and some who are no longer there. They don't get the credit they perhaps deserve.
"It is an unbelievable feeling to have signed for a club that has the stature of Leeds United. I am just looking forward to it and it wasn't a case of going to Leeds and playing in the Championship. We are looking to get into the Premier League and I want to be a part of that.
"It all happened fairly quickly but a club the size of Leeds United sells itself."