Horsfield, 35, has been training with the Red Imps in recent weeks after being given the all-clear after treatment for testicular cancer, with City boss Peter Jackson impressed by what he has seen.
He told the club's official website: "Everyone knows I'm looking for a striker and there's no better, bigger and stronger striker around at the moment on a free transfer than Geoff Horsfield.
"I know he's 35, but watching him train it's clear that he's still keen, enthusiastic and could be just what we're looking for.
"He hadn't kicked a ball in nine weeks before he joined us but I'm delighted to have him with us.
"He enjoyed his first week here, so we'll wait and see what happens over the course of the next couple of weeks or so."
Horsfield ended last season on loan at Glanford Park from Sheffield United.