The signing was initially stalled due to an issue with Coke's registration, but it has now been resolved and the midfielder is free to join the League Two side.
Talking to Grimsby's official website, Coke said he was 'absolutely delighted' to sign.
"It's been a tough week or two not knowing if I would be able to sign, but I am just so happy that it has been able to get sorted," he said.
"I have really been enjoying my time here so far. We have got a really good bunch of players now, especially with some new signings coming in which always lifts the place, so I personally am really happy looking at this squad and hopefully we can now start putting in performances to get results and get points onto the board.
"I have played at a good level for many years, so I am looking to bring in that experience. We have got a good mixture of young and old throughout the squad now so I think with a few good results we can really crack on and push up that table. The position of the club never put me off. I am always up for a fight and a battle, I have done that throughout my career and being here the last few weeks, not only is that my mindset, I can see it is with all the players and that is why I am confident we can turn this around."
Coke joins fellow ex-Hereford player Lenell John-Lewis at Grimsby.