Bellew, 29, has been playing local football but looked fit, sharp and hungry since linking up again with the Linnets squad this summer.
He has already had two spells with the club, and his most recent NPL club was Colwyn Bay.
Manager Michael Ellison said: " "What can I say about Warren?
"Everybody knows what he brings to the table - he's a real technician, he's got a wand of a left foot. He brings with him a wealth of experience and he's a great lad to have in and around the dressing room..
"I think it's safe to say we've not seen the best of him in his previous stints at the club but I'm positive that will change this season.
"He's in the best shape I've ever seen him physically and mentally and I'm delighted to have him on board."