The 48-year-old will take the reins following Edinburgh's final Magners League match of the season away to Benetton Treviso on Friday night, and brings with him a record of success in both a playing and coaching capacity.
As an international scrum-half, Bradley helped Ireland win the Triple Crown in 1985, and went on to feature in the 1987 and 1995 Rugby World Cups. In all, he won 40 caps for his country, captaining them 13 times. At club level Bradley won three leagues, three cups, and one All-Ireland title with Cork Constitution, his home-town club.
His first coaching role was with the Temple Hill outfit, from where he progressed to the role of head coach of the Ireland under-21 team, contributing to the progress of players such as Tommy Bowe.
Bradley then spent seven years as director of rugby at Galway-based Connacht, and helped establish the province as one of the best developers of young talent in European rugby as well as guiding the team to three Amlin Challenge Cup semi-finals.
His achievements at Connacht saw him receive the inaugural Magners League Chairman's Award for excellence in coaching in August 2010, where his outstanding contribution to the development of the Magners League brand and profile were honoured.
Bradley subsequently took on the role of technical adviser to the Georgia national team, working alongside former Scotland head coach Richie Dixon to see the side remain unbeaten in their 2010/11 European Nations Cup fixtures ahead of a Rugby World Cup meeting with Scotland in September.
Bradley previously spent five years as head coach of the Ireland A team, led the full side to New Zealand and Australia as head coach in 2008, and was an assistant coach on their 2006 trip to Japan.
Edinburgh chief executive Craig Docherty today welcomed him to the club, saying: "Securing Michael's services as head coach is great news and a real boost ahead of the new campaign.
"His experience of building successful teams and bringing through young talent will stand us in very good stead as we seek to continue to build the club. He is a proven leader, with pedigree in both the international and European arenas."
Scottish Rugby chief executive Gordon McKie confirmed: "I'm delighted to be welcoming Michael Bradley to Edinburgh. This appointment marks the culmination of an extensive recruitment process which saw an extremely pleasing level of interest in the post from a number of excellent candidates.
"Michael impressed everyone involved in the interview process with his passion for the sport and for taking Edinburgh forward. He has a track record of inspiring players to achieve, and offers vast experience gained in a number of different environments.
"I'd like to thank interim head coach Nick Scrivener for his efforts since Rob Moffat's departure, and wish Nick every success in his next role when he returns to Australia."
Bradley said he was "thrilled" to have been given a "massive opportunity", continuing: "I'm honoured and delighted to have been offered the chance to become the head coach at Edinburgh Rugby.
"I'm excited by the challenge of helping the club fulfil its potential, and I can't wait to start working with what is a talented squad. I know a lot of the players from my years in the Magners League with Connacht, and I'm well aware of their capabilities.
"I'm looking forward to spending the summer getting to know the club and the job, so that we're in a position to hit the ground running when the new campaign rolls round."
Commenting on the news, Andy Robinson, Scotland head coach, said: "This is a great appointment for Edinburgh and Scottish Rugby. I am certain Michael will bring great drive and determination to the role of head coach of Edinburgh. I very much look forward to working with him and wish him every success."
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