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The SFA said Strachan and his assistant Mark McGhee would leave “with immediate effect” to give his successor maximum time to prepare for the Euro 2020 qualifying campaign.
Scotland missed out on a place in the play-offs for the World Cup after drawing 2-2 away to Slovenia in their final group game last Sunday.
“I share the profound disappointment at missing out on the play-offs, especially having worked so hard to fight our way back into contention,” Strachan said in an SFA press release.
“The players should receive immense credit for that resilience in coming back from a difficult start and I would like to thank each and every player who has come in to represent their country.
“Together we have shared some really magical moments and those memories will live with me for ever.”
Former Scotland and Manchester United midfielder Strachan, 60, was appointed in January 2013 after Craig Levein was sacked following a poor start to World Cup qualifying.
Scotland missed out on a place at the 2014 World Cup and despite an improved showing in qualifying for Euro 2016, they came up short again.
Strachan’s position come under heavy scrutiny after they made a poor start to qualifying for the 2018 World Cup, but they rallied and finished the campaign unbeaten in their last six matches.
Scotland captain Scott Brown expressed disappointment about Strachan’s exit and suggested the players had hoped he would stay on.
“Sad sad sad day,” the Celtic midfielder wrote on Instagram.
“We all had faith in Gordon and believed in making the Euros. 14 points out of 18 in 2017 momentum was on our side.”
Scotland last participated in a major tournament at the 1998 World Cup.
The SFA announced Strachan’s departure after a board meeting at Glasgow’s Hampden Park.
“On behalf of the board I would like to thank Gordon for his excellent service to the national team,” said SFA chief executive Stewart Regan.
“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.
“After almost five years the board felt it was time for a new direction to prepare for the UEFA Euro 2020 qualifying campaign and also the forthcoming UEFA Nations League.
“We are grateful to both Gordon and Mark for their efforts and wish them the best of luck in the future.”
Strachan paid tribute to Scotland’s fans’ “unwavering support” and thanked his back-room staff and “everyone at the Scottish FA”.
He said the experience of managing the national team had been a “real privilege”.
Former Manchester United manager David Moyes is the early favourite to succeed Strachan with British bookmakers.
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