Bradley will continue in his role until the end of the season and admits that it has "been an honour" to manage the club.
Bradley told the club's official website: "It's been an honour to be Edinburgh Rugby head coach and I'd like to thank my fellow coaches, management team, players, staff, fans and sponsors for their support these past two years.
"Building a strong club with a clear identity, which has shared ownership from the players, management, fans, sponsors and the community at large is the key driver of all successful teams and, for me, it is critical that this work continues and enables both the club and the team to reach its full potential.
"The undoubted highlight of my two years was the joy on the faces of all connected with Edinburgh Rugby when the final whistle went when we overcame Toulouse in last year's quarter-final of the Heineken Cup at Murrayfield."
"I am very disappointed by the run of results this season and will put everything into the remainder of the season to help the club build for a brighter future."
Edinburgh lost all six of their recent Heineken Cup pool matches.