Robinson took the Scottish capital side to second in the Magners League this season and had been the favourite to take the top job at Murrayfield despite competition from former Springbok and Wallaby coaches Jake White and Eddie Jones.
The ex-Bath openside was previously head coach with England between 2004 and 2006 and had led the side to 41 wins from 50 internationals during an earlier role as assistant coach under Sir Clive Woodward.
"This is a wonderful opportunity for me to get back into Test rugby," said Robinson.
"I have enjoyed my time with Edinburgh immensely and to be appointed Scotland head coach is something that I am greatly honoured and excited about.
"I have enjoyed being part of the national and A team set-up in Scotland in the past two seasons and working with the players has fuelled my optimism. I am confident that I can take them and the national team onto bigger and better things.
"With the World Cup in New Zealand in 2011, I believe we have a crop of players who can really challenge the world's best and preparation for that starts now.
"I am very proud to be taking up the Scotland Head Coach role and I can assure all our supporters both at home and abroad that I will be doing everything I possibly can to bring success to the national team."
Robinson, who toured Australia as a player with the Lions back in 1989, will be supported in his new role by Scotland's current defence coach Graham Steadman, with further announcements regarding coaching staff expected in the near future.
Robinson's first challenge will be to lead Scotland A into the IRB Nations Cup in Romania next week, after which he will begin preparing the senior side for their autumn Tests at home to Fiji, Australia and Argentina.
"We are absolutely delighted that we have secured Andy Robinson as the new head coach for Scotland," said Scottish Rugby's chief executive Gordon McKie.
"Andy is an ambitious and highly-committed coach and I am confident that he will bring success to Scotland.
"Andy has proved himself at every level of the game and we are thrilled that he will now be leading the Scotland team as we look towards the challenges of the next three years, including the 2011 World Cup.
"He has been part of the Scottish Rugby family for the past two years and has brought success both to Edinburgh Rugby, with their highest ever Magners League finish in successive seasons, and has also guided the Scotland A team to notable successes.
"Andy has a well established relationship with many of the Scotland players and has an understanding of professional rugby at the highest level."