Strong, 53, spent four seasons as the Cardinals coach, going 37-15. Louisville posted double digit wins over the past two years, including bowl wins over Florida and Miami.
Strong took a program at Louisville that won just nine wins the two previous seasons and hadn't been to a bowl game in three years and took the Cardinals to four straight bowl appearances. The Cardinals won the Beef O'Brady's Bowl in 2010, the Sugar Bowl in 2012 and the Russell Athletic Bowl last week.
Strong takes over the Longhorns and will replace long time coach Mack Brown. Texas won the national title in 2005 but has not lived up to the high expectations in Austin of late. They were a pedestrian 18-17 over last four years in Big 12 play and 30-21 overall.
Strong has been an assistant at several high profile programs, including Florida (twice), South Carolina, and Notre Dame. He won two national championships with the Gators, serving as Urban Meyer's defensive coordinator.
Strong will become the 29th head coach at Texas.