The 62-year-old Dutchman, who also had a brief spell as Fulham manager between November 2013 and February 2014, has been appointed director of football methodology at Edgeley Park.
Stockport finished third in League One last season but fell short in the play-off final at Wembley, and have turned to Meulensteen partly for his top-level experience and partly because the role allows him to work closely alongside his son Joppe, who already coaches at the club.
His remit will stretch across both the academy and first team as Stockport look to build a consistent football programme from top to bottom.
Sporting director Damien Allen called the hire a landmark moment for the club: "Today marks a significant milestone in our club's history with the appointment of our first-ever director of football methodology.
"This landmark appointment reflects our commitment to building an elite football department, where every player and coach across the club is aligned behind a clear football philosophy, coaching methodology, identity and way of working. From the outset, we were determined to appoint someone with an exceptional track record of developing players.
"Throughout his distinguished career, he has played a key role in maximising the potential of world-class players, including Cristiano Ronaldo, and was an integral member of one of the most successful coaching teams in modern football, winning 11 major honours, including four Premier League titles and the UEFA Champions League."
Meulensteen, born in March 1964, spent 12 years at Old Trafford across two spells: an initial stint from 2001 to 2006, followed by a year away before he returned alongside Ferguson from 2007 until the manager's retirement in 2013. During that second spell he helped Manchester United win multiple Premier League titles and was on the touchline for their 2008 Champions League triumph.
He arrives at Stockport fresh from working as assistant coach with Iraq at this summer's World Cup, where the team was eliminated in the group stage, and his managerial CV also includes a period at Russian club Anzhi Makhachkala under former European Cup winner Guus Hiddink.