Despite being the overwhelming choice of the international players, Hadden still faced tough competition from Borders Reivers coach Steve Bates after Glasgow boss Hugh Campbell withdrew from the process.
The SRU have handed Hadden a contract up to and including the 2007 Rugby World Cup.
He said: "As a proud and passionate Scot this is the ultimate honour and one that I am determined to enjoy."
Hadden was praised by SRU chief executive Gordon McKie on his unveiling.
He added: "Frank hugely impressed our interview panel with the depth of his rugby knowledge, his coaching expertise and the vision he has for the national team.
"He is a man who understands Scottish rugby and understands what is required to get the best from our current group of elite players."
The SRU also confirmed Hadden will be staying on in an "overseeing" role with the Edinburgh Gunners for the time being.
McKie added: "During the transition phase, Frank will have an overseeing role at Edinburgh Gunners where there are very experienced coaches and players who will look to expand on the quite excellent start the Gunners have made to the Celtic League.
"As for the appointment of assistant coaches with the national team, that will be a matter for Frank to decide and I know he will be treating that as a priority."
Hadden has placed great emphasis on the Scotland team operating closely with the three regional teams and is upbeat about the future of the game in Scotland.
He continued: "We are where we are at the moment on the international rankings - ninth.
"It may be that our current position is a reflection of our current resources but we have a tremendous tradition in Scotland of over-achieving.
"I would not have taken this job if I had any doubts that we can restore that level of confidence in ourselves in the world game.
"People will inevitably ask me about targets and you have to be realistic. Look at our resources compared to the top five teams in the world.
"Our medium-term aim is to do well in the World Cup. When I sit down on a Monday to pick a team then I honestly believe that the team I pick is going to win the game and it's important that the players and supporters have that confidence too."