He will take charge this week and be in the dug-out for next month's friendly against Estonia before taking the national side through the remaining six World Cup qualifying ties.
Qualification already looks a lost cause – Scotland are bottom of Group A and eight points off the pace after only four games – but the 55-year-old will then start afresh when the Euro 2016 campaign begins next autumn.
The former Celtic manager, has been the frontrunner and outstanding candidate for the job since Craig Levein was relieved of his duties on November 5.
Negotiations have taken place with the SFA over recent weeks and over the past few days an agreement was reached with chief executive Stewart Regan.
Strachan, who won 50 caps for Scotland, enjoyed a largely successful period as Celtic manager between 2005 and 2009 but has been out of management since leaving Middlesbrough in October, 2010.
With Scotland's chances of qualifying for the 2014 World Cup effectively over, it seems likely Strachan would be given a contract through to 2016.
Should his appointment be confirmed, Strachan's first match in charge will be a friendly against Estonia at Pittodrie on February 6, before a World Cup qualifying double-header in March.
Scotland host Wales at Hampden on March 22 and face Serbia away four days later.
Strachan has made no secret of his desire to manage the national side. Speaking to ITV in November, he said: "It's quite simple really, it would be an honour to be asked to be the manager of your own national side, it's terrific.
"I could sit here and say 'yes, it would be great' or 'no, it's not for me' but it would also be arrogant of me to answer that if nobody has asked you and presume that someone will ask.
"Until you've been asked a question about a job, any job, then you really don't know how you'd go about it that's for sure. I wouldn't have the arrogance to think that someone is going to knock on my door."
Strachan could appoint Gary McAllister, his midfield colleague in the Leeds championship-winning side of the early 1990s, as his assistant.
Under-21 coach Billy Stark took charge of Scotland's last match, a 2-1 friendly win in Luxembourg in November.