The 27-year-old departed Tannadice to join Birmingham in 2011, but has now returned to United after leaving the Championship outfit in the summer.
United boss Jackie McNamara told Sky Sports News: "I know United fans will have great affection for Morgaro for what he achieved here previously but I have decided to offer him a contract based on what he has shown me over the last five weeks in training.
"His attitude, application and professionalism has been first class and added to the fact that he has excellent ability makes signing him an easy decision. Having him as part of the squad will allow me to select alternative tactics and formations at certain grounds and he brings great experience to the squad.
"This signing is very much about making the squad stronger and the length of deal will allow Morgaro and the club to see how the partnership can develop going forward."
Gomis came through the youth system at Chelsea.