The 23-year-old, equally at home on the wing or as a central striker, has signed a three-and-and-a-half-year contract at Bramall Lane and is determined to help the club win promotion to the npower Championship this season.
Motherwell manager Stuart McCall, who has already touted Murphy as a future international, played a key role in the player's decision to join the Blades, where he himself plyed his trade as a player.
Murphy, who has spent 11 years at Fir Park, said: "I hope if I'm playing well someone will take notice. I can maybe make a push for the Scotland squad, but it's up to me to work that little bit harder. I wouldn't say I'm under their radar, but I'm sure the first cap is the hardest to get.
"The gaffer (McCall) has only said fantastic things about the club. He said it's a great move for me and wishes me all the best, so it's great to leave on those terms. If he said to me it wasn't a great club, I don't think I'd be here. He means a lot to me, he's done a lot for my career, so I listen to his advice.
"Everyone wants to play at the highest possible level and I'm sure the club here are no different, so if I can be part of that then fantastic.
"I've never left the city of Glasgow to stay, so coming down here was a big decision, but it's definitely the right decision at this time and I'm looking forward to it.
"I'm an ambitious person myself and the club is (too). The club wants to push on and get higher and to be a part of that will be good."
Murphy could make his Blades debut at Oxford on Saturday in the third round of the FA Cup.