Scotland assistant coaches Stevie Scott and Duncan Hodge have been placed in interim charge. Bradley had been due to leave when his contract expired in May but the Scottish Rugby Union have announced that he and assistant Neil Back had agreed a deal to terminate their deals now.
Bradley departs Edinburgh following seven consecutive defeats in the RaboDirect Pro12, which leaves them in 10th place in the table, three off the bottom.
The Irishman led Edinburgh to the Heineken Cup semi-finals last season but they suffered six defeats this term, scoring just 36 points in the process. The former Connacht director of rugby was informed last month that his two-year deal would not be renewed.
Scott and Hodge will assume their roles after the RBS 6 Nations campaign ends, with Edinburgh not in action again until hosting Ulster on March 22.
SRU chief executive Mark Dodson said in a statement: "We feel this move is necessary to give a fresh impetus to the squad going into the remainder of the season. Our search for a new coaching team for Edinburgh Rugby continues, with a view to getting the club back on a winning track."
Edinburgh managing director Craig Docherty added: "It's heartening to welcome the appointment of two former Edinburgh Rugby and Scotland internationals to our backroom on an interim basis. I believe they are the right people to inspire our squad for the remainder of the season and assess the player group going forward."
Scott said he was "delighted" to get the opportunity to lead Edinburgh for the rest of the season.
He added: "Naturally the big thing for me at the moment is my commitment to the national team but, come a week on Saturday night in Paris, I'll be straight into Edinburgh Rugby mode and will be working with Duncan to get the players ready for the home match against Ulster and the rest of the season."
Hodge added: "As someone who played over 150 games for the club, I'm delighted to be given this opportunity to assist Edinburgh Rugby and have an influence on the last five games of the season."
- Sports & Recreation
- Edinburgh Rugby
- Duncan Hodge
- Scottish Rugby Union
- Stevie Scott