Initially, the appointment of Peter Young of Heriots' FPs is for a year but it is hoped that the post will become permanent.
Independent schools have traditionally been the breeding ground for top players but the SRU is keen to broaden the game's base. Mr Young will work with teaching staff at primary and secondary schools and introduce children as young as five to the sport.
Nearly a fifth of south-east Edinburgh's population of 105,000 are under the age of 17. "The south-east Edinburgh initiative has enormous potential and hopefully will quickly fulfil its educational and sporting promise," Mr Young said.
Jim Telfer, the SRU's director of rugby, said: "We would like to extend the game further into the state sector and communities where little rugby is played. Our message is that rugby has something important to offer youngsters, on and off the field of play."
Elizabeth Maginnis, the council's education convener, said it was "an exciting scheme building on the council's commitment to developing sport in education".