The 43-year-old, whose contract at Sheffield United had recently expired, replaces John Vaughan, who recently left the Galpharm Stadium to take up a similar role with Birmingham under Lee Clark.
Town manager Simon Grayson told the club's official website: "I know Paul from being on coaching courses with him, and having spoken to people who he's worked with he comes highly recommended.
"He's enthusiastic, hard-working and wants to make an impression here and do well - just like every other member of staff here.
"We also played together at Aston Villa for a short time and it does help to know him personally."
Crichton, who played for Peterborough, Doncaster, Grimsby, West Brom, Burnley and Norwich during a 24-year playing career, has coached at Gillingham, Cambridge United, Brighton and Norwich prior to his previous post at Bramall Lane.