Kwiatkowski has been the Huskies' defensive coordinator since 2014 after joining the staff from Boise State along with head coach Chris Petersen. He did not overlap at Washington with Sarkisian, who led the program from 2009 to 2013.
Kwiatkowski served as Washington's sole defensive coordinator in 2014 and 2015, shared responsibilities with Jimmy Lake from 2016 to 2019, and again held the sole coordinator title in 2020 after Lake succeeded Petersen as head coach.
"Husky Nation, In all my family's stops along my coaching journey it's always been about the people and relationships," Kwiatkowski posted Wednesday evening on Twitter without saying that he has taken the job at Texas. "... I hope I was able to make a positive impact on you and you did on me! I am going to miss you all! Until next time...... Go Huskies."
Kwiatkowski's hire has not been officially announced by Texas, but he changed his Twitter profile to include images of the Longhorns' logo and stadium.
The Football Brainiacs Texas first reported Kwiatkowski's hiring on Tuesday.
Mississippi State defensive coordinator Zach Arnett, Alabama defensive coordinator Pete Golding and others also were potential candidates for the Texas coordinator spot, according to sources. Former Rutgers coach Chris Ash served as Texas' defensive coordinator in 2020 under previous coach Tom Herman.
A former Boise State defensive lineman, Kwiatkowski began his coaching career at his alma mater in 1988, returned under Petersen in 2006 as defensive line coach and became defensive coordinator in 2010.
Between 2014 and 2019, Washington ranked seventh nationally in fewest touchdowns allowed (179) and ninth in yards per play allowed (4.86). In 2017, Kwiatkowski was a semifinalist for the Broyles Award, which goes to the nation's top assistant. In 2016, Washington's defense ranked eighth nationally in points allowed (17.7 PPG) and led the nation in takeaways (33) as the team made its only College Football Playoff appearance.