A spokesman for Averitt on Friday did not immediately return a call for comment from The Associated Press.
The tax consultant served nearly a decade in the Texas House before being elected to the Texas Senate in April 2002. Averitt chairs the Senate Committee on Natural Resources.
Democrats failed to field a candidate against Averitt. He was being challenged, in the March 2 GOP primary, by Darren Yancy of Burleson.
District 22 includes McLennan, Bosque, Coryell, Ellis, Falls, Hill, Hood, Johnson, Navarro and Somervell counties.