The 35-year-old Gomez is a 15-year veteran for New Jersey, the New York Rangers, Montreal, San Jose and Florida. Last season, he had 34 points, seven goals and 27 assists, in 58 games with New Jersey.
Gomez had 59 points in 2009-10 with Montreal, but his production has declined since then.
The Blues also invited Spencer Asuchak, Eriah Hayes, Zach O'Brien and Evan Trupp to training camp. The 27-year-old Hayes was the only player of those four to play in the NHL last season and had two penalty minutes in four games with San Jose.