The news comes following the United States Anti-Doping Agency's report that the American cyclist as well as Bruyneel had been part of "the most sophisticated, professionalised and successful doping programme the sport has ever seen".
A statement from RadioShack-Nissan said: "From this day on, Johan Bruyneel will no longer act in the position of general manager of cycling team RadioShack-Nissan.
"The reasoned decision published by the USADA included a number of testimonies as a result of their investigation. In light of these testimonies, both parties feel it is necessary to make this decision since Johan Bruyneel can no longer direct the team in an efficient and comfortable way. His departure is desirable to ensure the serenity and cohesiveness within the team."
Armstrong was stripped of his record seven Tour de France titles and handed a lifetime ban from the sport.