Kjaergaard, who competed in the 2000 and 2001 Tour de France on Armstrong's US Postal Service team, admitted in October last year that he took the banned blooster erythropoetin (EPO).
His admission came just before the US Anti-Doping Agency (USADA) published its devastating report that placed Armstrong at the heart of what it said was the biggest doping network in sporting history.
But the Norwegian anti-doping agency said in a statement that the Scandinavian rider would escape punishment as the time limit for bringing a prosecution had lapsed.
The facts of the case dated back to a period between 1998 and early 2003 — in other words, outside the eight-year statute of limitations, the body added.
Armstrong was banned from cycling for life and stripped of his record seven Tour de France wins in the wake of the USADA report which rocked the sport.
He subsequently admitted taking a cocktail of banned substances in a television interview with the US chat show host Oprah Winfrey.