Gillingham chairman Paul Scally gave Edinburgh his "full backing" earlier this season following a run of two wins in 14 league games, but the former Newport County boss failed to steer his side back up the table despite a fruitful November.
Defeats to Millwall and Oxford United over the New Year programme have now sealed Edinburgh's fate, with the Kent outfit expected to move quickly to bring in a replacement.
"Having returned to work yesterday, this is obviously a difficult decision to begin 2017 with," Scally told the club's official website. "I have been very keen to work with Justin and his coaching staff. I have become close friends with them over the past two years, and that is what makes this decision even harder.
"I have great respect for them and everything they have done for the club. I'd like to express my gratitude to Justin for his efforts; he has tried extremely hard to turn things around. However, the form over the past 12 months has not been as good as expected, and yesterday's defeat was the final straw. Nonetheless, Justin is a manager of great ability, and I have no doubt he will go far in football."
Next up for the Gills, who are eight points clear of the dropzone, is a trip to face Oldham Athletic on January 14.