Left back Powell signs on with the Hoops for another season while Ledwith joins from UCD and Murphy from St Patrick's Athletic
Ledwith, 21, joins from UCD after featuring as a regular for the Students during the 2012 Airtricty Premier Division season while Murphy, 27, is back at Rovers after a stint in goal for St Patrick's Athletic.
Murphy, a former Shamrock Rovers schoolboy who worked with manager Trevor Croly at Richmond Park, told the club's official website: "I'm delighted to be back at Shamrock Rovers. I spent a couple of years away from the club, but before that I was here for most of my career.
"I worked with Trevor at St Pat's last season and I'm looking forward to working with him again next season. I think Trevor is putting a good squad together and I'm delighted to be part of that."
And commenting on his re-signing, Powell said: "I'm really glad to be staying at the club. Last year was massively disappointing and I'm glad I'll get the chance to stay on and make amends for that. I think we'll have a very good side next year.
"It's good to have my contract sorted early. It can be an uncertain time for players, but now I can just concentrate on getting ready for next season."