It emerged earlier on Monday that the 23-year-old was at Elland Road to undergo a medical.
With an agreement having been reached with Crewe, he is now clear to step up into the Championship.
Murphy is a product of Crewe's famed academy system and made his senior debut for the Railwaymen while still in his teens.
He has gone on to become a first team regular, making close to 200 appearances over the last five seasons.
Murphy did not look out of place at League One level last season and will be looking to hit the ground running in the second tier with Leeds.
It is understood that Crewe will collect a fee of £1million as part of the deal.