The 32-year-old, who won last year's Grand Tour in Italy, said that he used performance-enhancing drugs over a decade ago, but asserted that it was a "short-lived" mistake.
"I have loved and lived this sport but more than a decade ago I chose the wrong path," read a statement from the Garmin-Sharp rider.
"Even though those mistakes happened more than 10 years ago, and they were short-lived, it does not change the fact I made them and I have lived with that and been sorry for it ever since.
"I believe that being truthful will help the sport continue to move forward, and over a year ago when I was contacted by anti-doping authorities, I was open and honest about my past."
Rasmussen - twice King of the Mountains at the Tour de France - claimed in his autobiography that he and Hesjedal took erythropoietin in 2003.