The 45-year-old takes over the Scottish side who have had a winless start to the Premiership season and a run of eight consecutive defeats. Critchley’s deal lasts until 2026-27 as he looks to turn the club around this season and drive them back up the table.
Critchley managed QPR but most notably Blackpool who he managed to win promotion to the Championship within his first season via the EFL League One play-offs.
Jambos chief executive officer Andrew McKinlay spoke about what an honour it is to work with the Englishman.
He said, "We've made no secret of the fact analytics has guided our search and that data presented us with many top-quality options.
"We were able to ascertain who would fit best into our new model going forward, which includes the use of analytics for recruitment.
"Neil understands well what we are looking to do, has experience at big club environments, none more so than at Liverpool, and is an ambitious coach."
Sporting director Graeme Jones also spoke on how the ex-Blackpool boss was the perfect candidate and how excited he is to work with him as the club aims to revive their season.
"I have been privileged to be involved in this process ahead of officially commencing my role and I have been impressed at how robust and concise it has been," added incoming sporting director Graeme Jones.
"Our analytics partners, who have an extremely good track record of managerial appointments in the UK and abroad, worked with us to provide a shortlist of compelling and contrasting options.
"Neil was the outstanding candidate based on the analytics and, having spoken with him at length, I believe he is who we need to provide success."