Lima, 31, was the 2011 Lance Todd Trophy winner as the Warriors won the Challenge Cup, and he left Super League at the end of 2012, having scored six tries in 61 appearances.
The former New Zealand international has won two NRL Grand Finals with Melbourne, and also played in the NRL for Wests.
Dragons coach Laurent Frayssinous said: “Jeff Lima is the ideal profile who fulfills all the criteria I was looking for. He is a consistent and aggressive prop and a real leader both on and off the field.
“The negotiations to sign him were hard but I’m delighted to sign a such quality player.
“He is a respected player in the Super League and NRL and he has a great experience of the big games. He will bring us a lot during the next three seasons.”