Lawrence told BBC Radio Kent: "I know Andy [Hessenthaler, Gills boss] from playing against him and the type of character he was.
"I guess I just wanted to work with that sort of person. I hope to come here and get promoted."
Lawrence started his professional career after leaving university by joining Wycombe in 1996 before spells with Fulham, Millwall, where he played in the 2004 FA Cup final, and Crystal Palace, where he was released at the end of the season.
I've been unemployed for two weeks, not quite signing on, it's been relatively worrying, but I didn't think my football was over
Matt Lawrence
But he does not think adjusting to League Two football will be a problem: "I've played about 15 games or so at this level, most of the time I've been playing League One and Championship. It will take getting used to I am sure but I am sure I will fit in.
"I am still fit. I started late, I've only played 550 to 570 games. I didn't think my career was over, I would have played anywhere. It's taken a while to find a club and get sorted.
"My contract ran out, I've been unemployed for two weeks, not quite signing on, it's been relatively worrying, but I didn't think my football was over."
Source: BBC Sport
Source: BBC Sport