Dooley replaces Josh Heupel, who left last month to become Central Florida's head coach.
Dooley, the 49-year-old son of former Georgia coaching great Vince Dooley, spent the past five seasons with the Cowboys after going 15-21 in three seasons as Tennessee's head coach. He was 17-20 as head coach at Louisiana Tech from 2007 to 2009.
"I am excited to be a Mizzou Tiger and look forward to helping Coach Odom carry out his vision for the program," Dooley said in a school release. "I am grateful for this opportunity, and am ready to get to Columbia and go to work."
Dooley served on Nick Saban's staffs with LSU and the Miami Dolphins.
Dooley played at Virginia and earned a law degree from the University of Georgia in 1994. He practiced law at a private firm in Atlanta for two years before getting into coaching.