The school announced the move late Monday evening ... explaining the coach's vax decision paired with state rules and regulations forced university officials' hands.

The school also said four of Rolovich's assistants -- Ricky Logo, John Richardson, Craig Stutzmann and Mark Weber -- were also being terminated over their refusal to get the shots.

"This is a disheartening day for our football program," said athletics director Pat Chun, who announced the team's defensive coordinator, Jake Dickert, would replace Rolovich. "Our priority has been and will continue to be the health and well-being of the young men on our team."

"The leadership on our football team is filled with young men of character, selflessness and resiliency and we are confident these same attributes will help guide this program as we move forward."

Rolovich has publicly been a staunch anti-vaxxer for months ... famously not showing up to Pac-12 media days in July over the conference's vaccine rules and regulations.

Rolovich had said at the time his reasoning for turning down the vax "will remain private" ... though it's since been reported the 42-year-old had been seeking a religious exemption.

Clearly, he didn't get it ... and with Washington mandating that its state employees get the vax -- Rolovich's time at Wazzu ended Monday.

"WSU students, faculty, and staff understand the importance of getting vaccinated and wearing masks so that we can safely return to in-person learning and activities," school president Kirk Schulz said.

"I am proud of all those members of our community who have set the example and taken the steps to protect not just themselves, but their fellow Cougs."