The 51-year-old, who won 30 caps for Scotland, was recently the director of Manchester United's youth academy.
"I am sure my experiences can be of benefit to Scottish football," said the former Motherwell and Celtic striker.
SFA chief executive Stewart Regan said McClair "has been at the cutting edge of coaching evolution, analysis and performance management".
McClair, who takes over the role following the departure of Dutchman Mark Wotte, spent almost 30 years at Old Trafford as a player, youth coach and director of the youth academy.
The SFA said he "was identified unanimously as preferred candidate during a recruitment process which involved the current Scotland national coach, Gordon Strachan, previous national coaches Walter Smith and Andy Roxburgh, as well as the Scottish FA's chief executive, Stewart Regan".
McClair begins in the role on 1 June and will be responsible for implementing the SFA's performance strategy.
He added: "I am extremely proud to have been given the responsibility to help Scottish football move forward as performance director of the Scottish FA.
"Having spent the majority of the last 30 years in England with Manchester United, I am looking forward to coming home, working with the coaching team at the Scottish FA and the clubs, and sharing the knowledge I have built up in that time to take on this new, exciting challenge."
Having started his playing career at Motherwell, McClair moved to Celtic in 1983 and went on to score 126 goals in 204 matches. He then joined Manchester United, where he made 471 appearances between 1987 and 1998. He scored 126 goals for the Old Trafford side and won four Premier League titles, one European Cup-winners' Cup, one European Super Cup, three FA Cups and one League Cup.
"The process of identifying a new performance director was thorough and hugely uplifting when we considered the quality of candidates," Regan added.
"Brian very quickly became a stand-out with his blend of experiences, not just from his trophy-laden career as a player at Manchester United, and his international contribution, but the depth of his coaching experiences with one of the biggest and most successful teams in the world.
"He has been at the cutting edge of coaching evolution, analysis and performance management at Manchester United and the recruitment panel were convinced he was the ideal person to lead the performance strategy into an exciting new era, enhancing the current provision while demonstrating the benefits of the investment so far to the future of Scottish football."
Brian McClair has been appointed performance director of the Scottish Football Association.