The 59-year-old has been confirmed in the role he held for 10 months in 2007, leaving for Birmingham in the November shortly after narrow failure to reach Euro 2008.
McLeish, who won seven of his 10 matches in charge first time round, said in a statement: “It is a tremendous honour to be named Scotland national team head coach.
“I am incredibly fortunate to have had the chance to lead my country already and I am immensely proud to be in this position for a second time.”
McLeish replaces his former Scotland and Aberdeen team-mate, Gordon Strachan, who lost his job after the nation’s exile from major tournaments passed the 20-year mark.
The former Rangers manager, who agreed a two-year contract, said: “There is much to be positive about in Scottish football, with players playing at the highest level and promising talent breaking through.
“With Hampden Park as one of the host venues for Euro 2020 we have an amazing opportunity to showcase our talents to the world from our own back yard. I am relishing the challenge of leading us to a major tournament and I cannot wait to get started.”
McLeish has been appointed 127 days after Strachan departed and only after Northern Ireland manager Michael O’Neill rejected the chance to take charge.
But SFA president Alan McRae insists the governing body has made the right choice.
“Alex McLeish is a true Scotland legend and a natural leader who has enjoyed success at club level in Scotland and England and at international level,” McRae said.
“It is a rarity to be in a position to appoint someone who has experience of successfully managing their country and we are delighted to reach an agreement with Alex.
“During the recruitment process he received resounding endorsements from several influential figures in the game which helped establish him as an outstanding choice from a strong list of possible candidates.
“Alex has demonstrated a desire and ability to get results with the national team and we believe that he is best placed to inspire our talented group of players to glory.
“With Hampden Park hosting matches at UEFA Euro 2020 it is more important than ever before for Scotland to qualify for a tournament finals and we believe that Alex is the exemplary candidate to guide us there.”