The midfielder, who was with Gillingham towards the end of last season, will be in the eighteen-man squad travelling to Barrow AFC tomorrow.
Muldoon came through the ranks at Charlton Athletic, earning himself a pro-deal in 2013.
While with the senior Addicks side, he had loan spells at the Gills, Dagenham & Redbridge and Braintree Town.
After leaving The Valley in January, he headed back to Priestfield – making four appearances in that time.
The 23-year-old had trained with the Stones during the summer and played for league rivals Dover Athletic in a Kent County Cup tie recently before agreeing terms with manager Jay Saunders.
Saunders said: “I am delighted to get Ollie on board. We were close to sorting something out over the summer but couldn’t get the deal over the line.
“We’d kept in contact and the timing couldn’t be better with the squad being so thin on the ground.
“At 23, he’s had a great grounding from his time at Charlton and still has plenty of years ahead of him. His arrival gives me options in the middle of the park and keeps the competition for places strong”.