Critchley's appointment at Villa Park leaves the Championship side looking for a new manager, which will disappoint them after their former boss' good work.
The 43-year-old knows Gerrard from his time working at Liverpool's academy where he coached the under-18s and under-23 sides.
He will replace Michael Beale, who left the Premier League club 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 says he is '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.
"Naturally, we are disappointed to lose him, but thank him for all that he has achieved during his time at Bloomfield Road and wish him well in the Premier League with Aston Villa.
"Our primary focus now turns to succession planning and making the best possible appointment to continue taking this great club of ours forward."