Murphy, 26, spent part of his youth career with Arsenal before signing a pro contract in 2009.
Loans spells with Brentford and Port Vale followed before he moved to Dutch side Telstar.
Murphy found his best form with Forest Green before joining York City and Crawley Town on loan.
Murphy played for England up to under-19 level and he was a part of the team that got to the final of the European Championships.
“He’s got a track record of scoring goals” said new United head coach Gary Owers. “We’ve done a lot of work to get him here, obviously we have got a bit of work to get him fitter. We’re looking for someone to get us a few goals at the top of the pitch and hopefully Rhys can be that person.
“I followed what he did at Forest Green at the beginning of last season – he got some goals pretty quickly. Mark Cooper has brought some forwards in that have got ahead of him.
“There were other clubs interested in him, but he has decided to come here which I am pleased about”.