The 40-year-old was finalizing a five-year contract worth nearly $3 million per season, reports Pete Thamel of Yahoo Sports.
The Cougars' job became vacant when Mike Leach departed for Mississippi State last week.
Rolovich is coming off his fourth year at Hawaii, where he's posted a record of 28-27. He led the Rainbow Warriors to a 10-5 mark and a division title in the Mountain West Conference in 2019.
He'll bring a new offensive scheme to a Washington State unit that was one of the most prolific in the country under Leach, who orchestrated the team's Air Raid system. The Cougars went 6-7 in 2019, but they averaged greater than nine wins over the previous years.