The 28-year-old former Arsenal trainee was released by North End at the end of last season.
He is no stranger to Meadow Lane having made nine appearances for the Magpies during a three-month loan spell from the Gunners between November 2001 and February 2002.
Short said: "I know I can put (Stephen) Hunt and Thommo (John Thompson) in the centre, and they have been outstanding, but I have always wanted another centre-half.
"I wanted a player who knows that position because it is such an important position. I spoke to him when I first got the job but he had a few options so he was weighing them up. I didn't think I would get him but luckily we have.
"Liam is not going to walk into the side and he knows that, but he will give us competition for places. It keeps players on their toes."