The 27-year-old, who was a member of United's Scottish Cup-winning team in 2010, left Tannadice in 2011 to join Birmingham.
Gomis has been training with United since September and has impressed manager Jackie McNamara with his enthusiasm.
McNamara said: "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, who came through the Chelsea youth system, has been a free agent since the summer - and he is delighted to return to Tannadice.
"The opportunity to get back playing at Dundee United makes me very happy," said Gomis.