Kelly, who is currently on the academy coaching staff at Premier League Sunderland, will take over the role on July 1 with Dean Holden becoming his assistant.
Holden had been in charge at Boundary Park since Lee Johnson left the club and took over at League One rivals Barnsley in February.
The club’s chairman Simon Corney said: “We are delighted to have in place a young, fresh and dynamic management team reflecting our ambitions on and off the field.
“From the moment we first met with him, Darren impressed the Board with his infectious enthusiasm, undoubted drive and energy and a confidence in his ability to deliver success for our football club.
“Coupled with his extensive coaching experience, knowledge of what is required to be successful in Football League One and a commitment to developing players at all levels we believe he is the right person to oversee the re-building of the football side of our club.”
Kelly added: “It is a role that I accept with immense pride and one which I am fully focussed on and committed to. As well as a wealth of playing and coaching experience, I pledge to Oldham Athletic and its supporters unwavering commitment and a desire to succeed.
“I am looking forward to building on the achievements of Oldham Athletic and driving the club to new levels of success. I ask the Oldham fans to believe in me and get behind the club whole heartedly as we embark on an exciting new era.”