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."

Shyan Wright wanted the 23-year-old to hide the gun because her "yard ain't hot", meaning police were not aware or interested in her home.
Wright, from Walsall, typed "God forbid the children getting closeâ€¦Lol" when the woman said she had stashed it and eight bullets in her room.
Wright, 25, was jailed for five years.
She denied aiding and abetting possession of a firearm but changed her not guilty plea to guilty at Birmingham Crown Court on Monday and was sentenced.
More updates on this story
Wright, from Forrester Street, asked her friend, whose children were aged two and three at the time, in a series of messages on WhatsApp in May 2015.
Using the name ShyShy, she said: "I need a big favourâ€¦me and my baby father was wondering if you could hold onto a [gun emoji] for a bit. Ur only one I can trust.", West Midlands Police said.
Three days later, she asked her where she had hidden it. When the woman confirmed "in Ma room", Wright joked about her children stumbling across it.
Officers raided the friend's home weeks later and recovered the weapon. She was subsequently jailed for five years, West Midlands Police said.
Detectives did not discover who ShyShy was until a wider gun crime investigation last year uncovered intelligence on Wright.
Her home was raided on 2 November when another phone was recovered that was shown to have been used in the WhatsApp conversation.
Det Con Damian Forrest, said both women had "found to their cost the catastrophic consequences of holding on to firearms for someone else".
He added "The messages 'laughing out loud' about what might happen if they '[the children] found the loaded gun are truly shocking and sickening."
Brian McClair has been appointed performance director of the Scottish Football Association.
[NEXT_CONCEPT]
A woman persuaded a friend to hide a loaded gun in her home and joked over WhatsApp whether her two young children might find it.