Kelly, who left his role at Boro three weeks ago, will work alongside County boss Michael Flynn, the club's management team and directors.
Speaking to the Newport website, Kelly said: "I’m delighted to be here as the club’s first-ever sporting director. I’ve had the privilege of working with two supporter-owned clubs that I’ve been at previously, so I’m looking forward to this new challenge.
"I share the same values as the football club and that’s important to me. When I was a player, I was always hard-working, honest and gave everything that I could, and those principles are the same at the football club.
"I’ve had good conversations with the manager and he’s someone who I’ve watched closely over the last couple of years. I’m very excited about the future and what we’re going to do, so hopefully we can achieve in the process."