The 58-year-old Kasich defeated Strickland with attacks over the loss of 400,000 jobs. The Democratic governor pointed to national economic factors and declining unemployment without success.
The new governor will help lead redistricting in the battleground state.
The fight hurt both Strickland and Lt. Gov. Lee Fisher, who led the administration's early job creation efforts. Fisher lost his bid for U.S. Senate Tuesday.
Kasich fought Strickland's attacks on his record as a managing director at Lehman Brothers, the failed investment bank. He promised to bring a more business-minded approach to the state's economy.