The 48-year-old, who won the Irish League with Linfield as a player and also starred for Portadown, Glenavon, Ballymena United and the Swifts, had taken over as interim boss following the departure of Dave Rogers in September.
Murphy was promoted from assistant manager into the temporary role but will now take charge of the Harps on a full-time basis, who finished the season in ninth.
He spent over three years in the Stangmore Park dugout and also held coaching positions at Linfield and Crusaders.
“I would like to thank Ian Harkin and the rest of the board for giving me this fantastic opportunity,” said the former Northern Ireland youth international manager. “After taking the team for the final six weeks of the season, it was something that I really, really enjoyed.
"So, when the opportunity arose to take the role in a full-time capacity it was something that I jumped at.
"The reasons behind the decision for me were that I wanted to challenge myself, I wanted to challenge the players and the fact that I have really enjoyed the last 12 months working at Finn Harps Football Club.
"I am grateful to be given the chance to explore the opportunity even further.
"I have thoroughly enjoyed working with all the people around the club and most importantly I have enjoyed working with the players.
"I would also like to acknowledge that the supporters and the people around Donegal have been fantastic to me since I arrived.
"I hope to confirm some appointments of my backroom team in the next short while.
"Finally, I am really looking forward to the challenge and what I would like to say to the Finn Harps fans is that I will give the role 100% and I will do the best that I can to put a team out on the pitch that they are proud of.”