The 45-year-old Kragthorpe, who interviewed with Miles earlier this week, will replace Gary Crowton, who left the program last week to become Maryland's offensive coordinator.
"This is a great opportunity to join the coaching staff for one of the top programs in college football and to compete in a league as strong and competitive as the SEC," Kragthorpe said.
Miles is hoping the arrival of Kragthorpe will boost the Tigers' quarterback play in particular. The Tigers were 11-2 last season despite ranking 86th in total offense and 107th in passing.
Last month, however, Miles signed 6-foot-5, 230-pound junior college transfer quarterback Zach Mettenberger, a former top Georgia recruit who was dismissed by the Bulldogs because of legal trouble.
"Steve brings to our staff the type of experience necessary to develop quarterbacks," Miles said. "He's an experienced play-caller who will bring a great deal of enthusiasm and energy to the staff."
Kragthorpe, a former Buffalo Bills quarterbacks coach earlier this decade, was 44-43 in seven seasons as coach at Tulsa and Louisville after leaving the NFL.
Former Florida quarterbacks coach Scot Loeffler, one of the other candidates who had interviewed for the LSU job, had received strong consideration.
After taking over for Bobby Petrino in Louisville in 2007, Kragthorpe went 15-21 during three seasons. Before that, he was 29-22 in four seasons at Tulsa and was only the second coach to lead the Golden Hurricane to three bowl games.
He began his coaching career as a graduate assistant at Oregon State in 1988 and in 1996 served as Boston College's quarterbacks coach. There, he worked with Matt Hasselbeck, who has since flourished in the NFL with the Seattle Seahawks.
Kragthorpe went on to serve as offensive coordinator at Texas A&M and as quarterbacks coach for the Buffalo Bills before taking over at Tulsa in 2003.
Information from ESPN The Magazine's Bruce Feldman and The Associated Press was used in this report.