Critchley had been in charge of Liverpool’s academy for the past six-and-a-half seasons but now leaves for Blackpool on a three-and-a-half-year contract.
Critchley replaces Simon Grayson, who was sacked as Blackpool manager last month following a run of one win in 12 games.
The 41-year-old has been thrust into the limelight at Anfield this season, taking charge of a youthful Liverpool side against Aston Villa in the Carabao Cup quarterfinal in the December while the senior team were away at the FIFA Club World Cup in Qatar.
Critchley was also in charge of a young Liverpool side that eliminated Shrewsbury town in the FA Cup fourth round replay at Anfield last month during the Premier League’s winter break.
Liverpool academy director Alex Inglethorpe told the club's official website: "It’s a bittersweet day in many respects.
"Obviously losing a person and professional of Neil’s calibre is something that is a disappointment, but at the same time we have great excitement and joy that he has been given this wonderful opportunity.
"We see this as a reflection on the Academy as a whole, that it's an environment where players and coaches have a pathway to progression and self-improvement.
"Blackpool want Neil because of the work he's done at Liverpool and it shows to everyone within our system that if you work hard and work smart then rewards are there.
"Neil epitomises the best qualities of a modern coach: leadership skills, intelligence, compassion and a hunger for individual and collective improvement. Blackpool are very fortunate to have him and we wish him well."
Blackpool lie in 13th place in League One.
