He will replace Michael Beale, who leaves to take up the position as QPR's new manager.
Critchley was a huge success at Bloomfield Road following his March 2020 appointment, guiding the club back to the Championship via the play-offs in his first season in charge before consolidating their position in the second tier.
Blackpool owner Simon Sadler said he was 'disappointed' by Critchley's exit.
He said on the club website: "Neil has been a consummate professional ever since arriving at Blackpool and really bought into what this club and town are all about.
"He has built up strong relationships with the staff, players and supporters and made some special memories for us all.
"Our primary focus now turns to succession planning and making the best possible appointment to continue taking this great club of ours forward."