Connecticut-born Murphy latterly worked as the technical director at DC United and prior to that, he was the technical director at Real Salt Lake and head scout at New York Cosmos.
The 33-year-old is the full-time replacement for Gauthier Ganaye, who left the club to join Nice at the start of February, with co-chairman Paul Conway assuming CEO duties for an interim spell after the Frenchman's departure.
Murphy started his professional playing career with DC United and went on to play in 2. Bundesliga for VFL Osnabrück from 2009-2010 before returning to the US to play for the Cosmos in the North American Soccer League (NASL).
On his appointment, Murphy said: He said: “I am delighted to be joining Barnsley Football Club. Few from America have the opportunity to work in English Football, let alone a storied club with a rich history of success.
"In my short time within the Barnsley community it is quite clear that nothing is given, and everything is earned. I have travelled enough of the world to recognise true passion and those that fight for what they have, which is evident in the culture of the Barnsley people.
"Through hard work and diligence, I hope to help give the Barnsley faithful everything they deserve and a team to be proud of. I am confident that the squad and coaching staff led by Daniel Stendel will bring joy to Oakwell this season and those beyond. “As well as on the pitch, we will be looking to continue the good work off it. The club has a number of plans and ideas in place, with the fans at the forefront of this. I am thoroughly looking forward to meeting with our fanbase and seeing how we can work together to make Barnsley a club that everyone wants to be a part of.”