The Scottish FA announced that Strachan would not continue in the role after Scotland's World Cup hopes ended with a 2-2 draw in Slovenia on Sunday.
A 2-2 draw in their final qualifier against Slovenia last week was enough to see the Scots fall short of reaching Russian Federation 2018 on goal difference, with Strachan left to rue his side's genetic deficiencies in the aftermath.
Graeme Sharp, the former Scotland striker, cast doubt yesterday over whether David Moyes would take charge of the national team.
Strachan was appointed as Scotland manager in January 2013 but has failed to qualify for a major tournament during his tenure as national team boss.
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The decision was one of mutual consent with assistant Mark McGhee also leaving his job.
SFA board members gathered at Hampden Park on Thursday afternoon for a meeting at which Strachan's future was discussed.
"I share the profound disappointment at missing out on the playoffs, especially having worked so hard to fight our way back into contention", Strachan said.
Together we have shared some magical moments and those memories will live with me forever.
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He said: "The players in there, I've got to look after them. It has been a real privilege".
Scottish FA chief executive Stewart Regan said: "On behalf of the board I would like to thank Gordon for his excellent service to the national team". I know how disappointed he was that we couldn't secure a play-off place but to come so close was a tribute to the belief he instilled in his squad.
"We are grateful to both Gordon and Mark for their efforts and wish them the best of luck in the future".
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