The 36-year-old, who was recently released by Hartlepool, returns to Boundary Park having scored 15 times in 105 appearances for the club between 2001 and 2004.
The move comes with Latics boss Paul Dickov short on midfield cover due to Dean Furman's absence with South Africa at the African Nations Cup and injuries to Cristian Montano and Youssouf M'Changama.
Dickov told his club's official website: "Paul will add experience to the squad that will be invaluable to the young kids. I am delighted to have him on board and he will be another body in our squad."
Murray added: "I am here to help in whatever I am asked to do. And the club knows what they will get from me. I am experienced and still have the desire and enthusiasm to play.
"I may be 36 years of age but I am as fit as any time in my career and am looking forward to getting my teeth into things here."