The Murrayfield club have also revealed that defence coach Billy McGinty has left the club already after resigning from his post.
Bradley will continue to coach the side until his contract ends in May and will share the defensive duties with forwards coach Neil Back.
The Irishman told the club's 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."
The decision not to renew Bradley's deal has come as little surprise following a wretched season. The capital outfit lost all six of their Heineken Cup matches and currently sit fourth from bottom in the RaboDirect Pro12.
Scottish Rugby chief executive Mark Dodson confirmed a search for a new boss will begin "immediately".
He added: "Michael and Billy have played a pivotal role in a number of memorable games at Murrayfield. In particular, last year's journey to the Heineken Cup semi-final in Dublin was a highlight. This season's results, however, have been below the standards expected by the club and its fans and we believe the time is right to begin the search for a fresh coaching team."