Murphy is the second signing for the Blades in as many days after the League One promotion hopefuls sealed a deal with Danny Higginbotham on Wednesday.
The 23-year-old, who can play on either wing or as a central striker, finalised his move for an undisclosed fee to Bramall Lane after Motherwell's 1-0 defeat by Celtic.
Murphy had an eventful game at Celtic Park, winning a late penalty for the visitors, and Blades boss Danny Wilson is more than happy to have landed the player.
Wilson said: "We are absolutely delighted to have secured a deal to bring Jamie to Sheffield United because the lad is a real talent.
"He is quick, strong on the ball and a good runner in possession. He will put defenders on the back foot and will offer us great versatility in forward positions.
"Jamie has a real eye for goal and will give us that bit extra quality that we need to unlock some stubborn League One defences."