Gibbs, a former Houston Texans secondary coach, had earlier Monday announced his departure from the Cougars program.
"I couldn't be more excited about joining Coach Kingsbury and the rest of our coaching staff," Gibbs said in a statement. "I have followed Kliff's career and believe special things are happening in Lubbock. There are several talented, young defensive players that will contribute for years to come. I am grateful for this opportunity and look forward to getting started soon."
Zac Spavital, a defensive assistant with Houston, also will join the defensive staff, while running backs coach Mike Jinks was promoted to associate head coach, Texas Tech said.
"I am extremely excited to have Coach Gibbs and Coach Spavital join our staff," Red Raiders head coach Kliff Kingsbury said in the statement. "What they were able to accomplish in their short time at the University of Houston is incredible."
Gibbs' defense for the Cougars came up with 73 turnovers this season, the most of any team in the FBS. Texas Tech has been among the bottom 10 in the nation in turnovers.
Gibbs served as the Cougars' interim coach for the Lockheed Martin Armed Forces Bowl in Fort Worth, Texas, last week following the firing of Tony Levine. Houston won 35-34, overcoming the largest fourth-quarter deficit in a bowl game to win in regulation.
Texas Tech's defensive coordinator position had remained vacant since Matt Wallerstedt abruptly resigned Sept. 18 after sources told ESPN.com the coach was suspected of being under the influence of an unknown substance while on campus.
Kingsbury replaced Wallerstedt on an interim basis with Mike Smith, who had been coaching linebackers.
Smith returns to his role as co-defensive coordinator with Gibbs' hire.
Gibbs, 46, was the secondary coach for the Texans for the 2009 and 2010 seasons. He was defensive coordinator at Auburn in 2005 before becoming defensive backs coach for the Kansas City Chiefs from 2006 to 2008.
A Colorado graduate, Gibbs also has been an assistant at Colorado (1993-94) and Kansas (1995-96) and was defensive coordinator at Minnesota from 1997 to 2000. Gibbs also was a defensive assistant with the Denver Broncos from 2001 to 2004.
"With stops in both college football and the NFL, coach Gibbs will bring experience and ingenuity to our defensive unit," Kingsbury said in the statement.
Gibbs is the eighth defensive coordinator for the Red Raiders since 2007. A Texas Tech spokesman said Gibbs will have a two-year contract worth $550,000 a year.
Information from ESPN's Brett McMurphy and The Associated Press was used in this report.