The former Celtic and Middesbrough boss replaces Craig Levein, who had presided over a disastrous start to the Scot's 2014 World Cup qualifying campaign in his three-year spell
Levein was sacked in November by the SFA, and will be replaced by the former Celtic and Middlesbrough boss, who was capped 50 times by the Scots.
Strachan makes his first return to management since leaving Middlesbrough in October 2010 by mutual consent.
“I am extremely proud to be appointed as Scotland National Coach," he told the Scottish FA's official website. "There is a considerable challenge ahead in the World Cup qualifying campaign but we can take those first steps towards addressing that in the double header against Wales at Hampden and the visit to Serbia in March.
He added, “Next month’s match against Estonia will give me an opportunity to assess the squad and, of course, it will be an unforgettable experience walking out as Scotland National Coach at Pittodrie, a stadium that holds many special memories as a player.
“I can assure the supporters that I will do everything in my power to make sure we have a national team we can all be proud of and one that, in time, can experience the excitement of participating in a major championship finals once again.”
Levein had been in charge of Scotland for three years, and had made a poor start to its World Cup 2014 qualification campaign, leaving it bottom of its group with no wins.
He also presided over their Euro 2012 qualifying campaign, when the country finished third in its group, just two points away from the playoffs.
In response to Strachan's appointment, Stewart Regan, chief executive of the Scottish FA said: “We are delighted to have appointed Gordon as the new Scotland National Coach.
"As a player, his style and swagger made him a huge favorite of the Scotland supporters and few can forget his celebration against West Germany in Mexico in 1986.
“As a manager, he has experience at the highest level in England and Scotland, most notably taking Celtic into the last 16 of the Champions League.
"Within minutes of meeting Gordon to discuss the possibility, we were left in no doubt that he was the man to help rejuvenate our FIFA World Cup Brazil 2014 Qualifying campaign, starting with the March double header against Wales and Serbia."