The 21-year-old has been on trial at the club for the past week and his performances have resulted in him earning a deal at MEMS Priestfield Stadium.
Nash scored twice against Chatham Town on Tuesday evening and won a penalty against Dover at Crabble last weekend, a game which finished 2-2.
The striker scored 37 goals last season for Maldon and Tiptree, resulting in increased speculation regarding his future; however he is now officially a Gills player.
On signing for the club he said: “The way the fans have supported me over these past couple of games is very welcoming.
“I’ll give 100 per cent back to them; I’m going to put the effort in to get my starts and do my hardest to get the ball in the back of the net.”
Manager Ady Pennock said: “We are delighted to sign Liam; he has been fantastic in training and his performances in the games we have played have been impressive.
“The fans took to him instantly and we now look forward to working with him.”
A full interview with Liam will be on iFollow shortly, where you can also see exclusive interviews with Conor Wilkinson and Connor Ogilvie.