Robins boss Mark Yates told BBC Radio Gloucestershire: "Steve's been on the radar a long time because I met him two days after last season finished.
"I'm delighted to have got such a good organiser and a real leader."
Elliott becomes Cheltenham's ninth summer signing, and will add valuable experience to a squad with an average age of 23.
Yates added: "The chairman and the board have to take a lot of credit for this. They've seen a player that we wanted to bring to the club, and they've pushed the boat out a bit to get him.
"I don't mean that stupidly, but they've allowed us to do it and it's a big positive for me and my staff."
Source: BBC Sport
Source: BBC Sport