Greece striker Dimitris Salpigidis has said playing for the club, who clinched a spot in the Champions League preliminary round for next season, was like being "in the jungle" as angry fans protested and players had their cars vandalised.
Dutchman Stevens, who has signed a two-year contract with PAOK, is hoping to create a team that fans can feel proud of.
"PAOK is a team which represents hard work and I always have felt comfortable at such clubs. I like the work ethic and my goal is for all us to help PAOK to take steps forward," the 59-year-old told the club's website.
"I think it is very important that the fervent supporters are united and give the team their full backing, to feel that it is something which truly belongs to them.
"We will do everything in our power to create a competitive team, a team that they can feel proud of."
Stevens has a wealth of experience in German and Dutch soccer, having coached the likes of PSV Eindhoven, Hamburg SV, Hertha Berlin and Schalke 04.
PAOK are the country's biggest club outside Athens but last won a league title in 1985. Their last trophy success was a Greek Cup win in 2003.
They scrambled through to the third qualifying round of Europe's elite club competition after a 2-1 win over PAS Giannena in the final match of the Super League playoffs earlier this month.
The season featured regular protests at the Toumba Stadium and at the training ground, leaving players feeling frightened.
"These are not the sort of conditions to play football in when at any time you feel someone may come to try and kill you," Salpigidis told reporters this month.