The Motherwell boss, who has been named assistant national coach, joins Fir Park predecessor Mark McGhee in the role following his appointment last week.
McCall, a former midfielder with Everton and Rangers, scored one goal in 40 matches for Scotland between 1990 and 1998.
In a statement, the 48-year-old, who has led Motherwell to the Scottish Cup final and Champions League qualifiers, said: "I am thrilled to have been asked by Gordon to join his backroom team.
"Playing for my country was the highlight of my career and I've been fortunate enough to play at World Cups and European Championships.
"They hold special memories for me and the Scotland supporters deserve a return to those days.
"I am proud to be asked to assist with the national team and look forward to working with an excellent squad of players and two outstanding coaches in Gordon and Mark."
Former Celtic boss Strachan said: "In many ways Stuart typified the classic Scotland international player. He was passionate and combative but was also hugely influential and inspirational.
"He has done a tremendous job at Motherwell and his knowledge of the game, especially of the Scottish scene, will be invaluable.
"I am excited about working with Mark and Stuart and I am sure the players will benefit from their coaching experience."