The 55-year-old has not worked in management since leaving Middlesbrough in October 2010, but is now set to replace Craig Levein, who was sacked by the Scottish Football Association in November 2012 after a run of poor results.
Scotland are currently bottom of Group A in the 2014 World Cup qualifying campaign after defeats to Belgium and Wales in October last year.
Strachan's first game in charge is likely to be a friendly against Estonia next month at Hampden Park.
Strachan, who won 50 caps for Scotland between 1980 and 1992, played for his country in the 1982 and 1986 World Cups in Spain and Mexico, respectively.
He began his managerial career with Coventry City in 1996 and helped to save the club from relegation with a last-day win at Tottenham in the 1996-97 season.
Strachan won three successive Scottish Premier League titles with the Parkhead club and became the first manager to take them beyond the Champions League group stages in the 2006-2007 season.
He missed out on a fourth SPL title in 2009 and stepped down from his post with the club.
Strachan joined Middlesbrough in October 2009, but after an unsuccessful stint with the Championship side he resigned a year later. However, Strachan refused any compensation from the Teesside club, as The Guardian reported at the time.