Hodge, the former Scotland stand-off, has spent the last 12 seasons with the capital club.
Blair’s background as a backs and attack specialist has meant Hodge has been allowed to leave. The club said he had left “on amicable terms”.
Hodge said: “I have greatly enjoyed my time coaching in various roles in Scottish Rugby over the past 14 years.
“It has allowed me the opportunity to work across a wide range of age groups and playing levels, and to develop my knowledge and experience through working with 11 different head coaches throughout the period.
“I feel extremely lucky to have worked with some world class coaches, players, and teams and thank them for their support over the years.
“Coaching at three Rugby World Cups, competing in Pro14 and Heineken Cup semi and quarter finals along with seeing so many Edinburgh players recently progress to Scotland honours has certainly given me plenty of fond memories to look back on.
“I look forward to using this experience as I move on to new opportunities in the next stage of my career.
“Finally, I would like to wish Mike and the rest of the team all the very best for the upcoming season and beyond.”
Blair, who was appointed head coach of Edinburgh last month following the departure of Richard Cockerill by “mutual consent”, said: “Duncan deserves a lot of credit for his part in developing quality Edinburgh players for the club and the national team over the years. Everyone at the club thanks him and wishes him well.”
Hodge had two spells as a player with Edinburgh and his coaching connection with the club began in 2007, when then Scotland head coach Frank Hadden enlisted his services as a part-time specialist coach across Edinburgh, Glasgow Warriors and the national team, a role which became full-time in 2012.
He was promoted to assistant coach in Vern Cotter’s Scotland set-up for a two-year spell, which included the national team’s route to the Rugby World Cup quarter-final, where they were edged out by Australia in the dying minutes.
He was also assistant to Shade Munro when Scotland A pulled off an impressive 13-9 away win over England Saxons at Kingston Park.
Hodge then returned to Edinburgh as assistant coach, where he has remained in post for the past five seasons, including a short spell as interim head coach.
Edinburgh Rugby managing director, Douglas Struth, said: “I would like to thank Duncan for the considerable and lasting contribution he has made to the club and its players across various roles.
“As a player, Hodgey captained the club, and as a coach he has played a major role in the development of scores of Edinburgh and Scotland players over the years.
“We would like to express our sincere respect and gratitude for everything he has done for the club.”