Board members met at Hampden on Thursday morning with the 60-year-old's future the most pressing issue.
The decision was taken to relieve him of his duties as boss of the national team with pressure mounting ahead of the crucial Euro 2020 double header against Belgium and Cyprus in June.
McLeish oversaw the 3-0 defeat in Kazakhstan in the opening fixture of Group I, putting the country in a difficult position to qualify directly for next year's tournament after only one game.
It was followed by a sterile 2-0 win over minnows San Marino, a game which saw the side booed and chants directed towards the SFA board.
Coaches Peter Grant, James McFadden and Stevie Woods have also left their positions with Scotland.
Ian Maxwell, Scottish FA chief executive said: “On behalf of the Board, I would like to place on record my thanks to Alex and his backroom team for their efforts in leading the national team over the past 12 months, not least in topping our UEFA Nations League group and reaching the play-offs.“The decision to part company was not an easy one, especially given Alex’s status as a Scotland Hall of Fame member, earning 77 international caps, having played in three World Cups and taken charge of the national team for two spells.“It was only taken after full consideration by the Board and after an honest and respectful conversation between myself and Alex earlier in the week. Ultimately, the performances and results as a whole in the past year – and, in particular, the manner of the defeat in Kazakhstan – did not indicate the progress expected with a squad we believe to be capable of achieving more.“With that in mind, it was agreed that we would seek to recruit a new management team to take us forward for the remainder of European Qualifying campaign.“At this point I would like to pay tribute to Alex for the good grace with which he has accepted the decision and for remaining unstinting in his support of the team for the remainder of the campaign. It befits his status as a Scotland legend and Hall of Fame inductee.“We firmly believe we have the potential to recover from the opening group defeat and unlock the potential of this exciting squad of players for the remainder of the campaign, safe in the knowledge we also have the play-offs as an additional route to UEFA EURO 2020.“With Hampden Park one of the Host City Venues for the 60th Anniversary of the European Championships, we are determined to ensure our supporters can watch the national team participate in UEFA EURO 2020.“Alex, Peter, James and Stevie leave with our best wishes for continued success in the future.”Alex McLeish said: “I am grateful for the opportunity to have managed my country for a second time and leave knowing that I gave my all in the pursuit of success. I am proud that together we finished top of our UEFA Nations League group and qualified for the UEFA EURO 2020 play-offs, which gives us a real opportunity to reach a major tournament for the first time in over 20 years.“I am also pleased to have given many younger players a first taste of international football that will stand them – and the country – in good stead for the future.“I would like to thank those players who showed a passion for wearing the dark blue, my assistants, Peter, James and Stevie, for their contribution over the past year. I would also like to extend my gratitude to the entire national team backroom staff and my friends and colleagues at the Scottish FA.“Finally, I would like to thank the Scotland fans for their unwavering support of the team and look forward to taking my place among them in the future.”
The former Aberdeen defender was appointed Scotland boss for the second time in February 2018 on a two-year deal, taking over from Gordon Strachan.
He led the side to the top of the Uefa Nations League group, ahead of Israel and Albania which ensures Scotland have at least a playoff opportunity to qualify for the tournament next year with Hampden Park one of the venues.
The sacking adds to McLeish's difficult managerial record over the past seven years.
Since leading Birmingham City to League Cup success against Arsenal in 2011 he has overseen their relegation from the English top-flight, a difficult time at rivals Aston Villa before equally disappointing spells with Nottingham Forest, Genk and Zamalek.
The Scottish FA will now look to candidates for the games in June with Strachan, Kilmarnock boss Steve Clarke and David Moyes among the favourites.