The Scottish FA said on Friday the former Manchester United and Leeds United midfielder had signed a two-year contract extension.
"It is an honour and a privilege to manage my country and, in a way, that has made the disappointment of not qualifying for Euro 2016 all the more profound," Strachan said in a statement.
"I want the best for our country and for those players and I believe we can make Scotland proud in the upcoming qualifiers.
"For that reason, I am delighted to have been asked to continue in my role and I look forward to working with my backroom staff and the players to improve on the previous campaign and look forward to the World Cup qualifiers with optimism."
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Strachan, who earned 50 caps for Scotland during his playing career, has been in charge of the national team for 25 games, winning 12 and losing eight.
Scotland finished fourth in Euro 2016 qualifying Group D, behind Germany, Poland and Ireland.
England are one of Scotland's opponents in qualifying for the 2018 World Cup in Russia.
(Reporting by Martyn Herman, editing by Ed Osmond)
