After missing out on top target Michael O'Neill, who instead opted to remain on as Northern Ireland boss, Scottish football chiefs turned their attention to Alex McLeish.
The former Aston Villa, Birmingham City and Rangers manager said he is eagerly looking forward to linking up again with the national team.
McRae said: "Alex McLeish is a true Scotland legend and a natural leader who has enjoyed success at club level in Scotland and England and at worldwide level".
McLeish will replace Gordon Stracham who left the position in October due to Scotland's poor performance in qualifying for the 2018 FIFA World Cup.
His first match in charge of Scotland will be at Hampden Park on Friday, March 23 against Costa Rica, followed by a trip to Hungary four days later.
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McRae said: "During the recruitment process he (McLeish) 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".
McLeish, 59, won seven of 10 games in charge during his previous spell in 2007, including a famous 1-0 win away to France, as Scotland narrowly missed out to Italy for qualification for Euro 2008.
Meanwhile, Stoke City midfielder Charlie Adam said he was "delighted" to see Mcleish get another chance to manage Scotland.
New Scotland boss Alex McLeish has vowed to win over the doubters by ending the Tartan Army's wait to attend a major finals.
Former boss Walter Smith was next to turn down the role as the search widened. "I'm up for the challenge and I believe that I'm the right guy for the job".