During his first spell in charge in 2007, McLeish led Scotland to seven victories in 10 matches before joining Birmingham City.
"It is a tremendous honour to be named Scotland national team head coach," McLeish said in a statement.
"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.
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"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."
Former Scotland defender McLeish, who was capped 77 times, has also managed Aston Villa, Nottingham Forest, Belgian side Genk and Egypt's Zamalek.
"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," Scottish FA president Alan McRae said.
"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."
McLeish's first games at the helm will be friendlies against Costa Rica and Hungary next month before Scotland face Peru in May and Mexico in June.
His competitive debut will come in the UEFA Nations League against Albania on Sept. 10.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
