Koeman succeeded Mauricio Pochettino as Southampton boss earlier this month, with the former's brother Erwin and Jan Kluitenberg also taking up coaching roles at St Mary's Stadium.
Lee, a former manager at Bolton Wanderers best known for his time as a player and coach at Liverpool, has now been appointed as first team assistant coach.
Southampton have also brought in Dave Watson, England's goalkeeping coach, while Martin Hunter has been appointed as technical director after four years in charge of the club's development squad.
Executive director Les Reed said: "I am extremely happy that we have been able to appoint three highly-respected and talented coaches to these important positions in our coaching structure.
"That we have been able to attract Sammy and Dave to Southampton is testament to our ambition to continue growing as a club, and shows our commitment to develop talented footballers at all age levels.
"Sammy has a wealth of experience from his time with Liverpool and Bolton, as well as from his long association with the England team (as a coach under Sven-Goran Eriksson).
"He will work closely with Ronald, Erwin and Jan, and will play a big part in the day-to-day coaching of the first team."
