The 28-year-old has been without a club since leaving Cheltenham at the end of January and has agreed to help the Shots' survival bid.
Goulding scored 19 goals in 111 appearances for the Robins after signing from Bournemouth in 2010. He scored three times in 23 games for Mark Yates' side this campaign before being released by mutual consent.
Manager Dean Holdsworth told the club's official website: "Jeff is hungry to play games and prove a point. He was part of a successful Cheltenham team in this division and he can be a handful too."
Goulding joins a club currently in the relegation zone with 15 games remaining, but within two points of three of their rivals.