The personal admission was made to Hushovd before Armstrong went public with a confession to Oprah Winfrey.
"We had started talking about the accusations from Tyler Hamilton when Lance, with no prodding, admitted to doping," Hushovd wrote. "It was possible he noticed that I was stunned, because he looked at me, pulled his shoulders back and said, 'Thor, everyone does it.'"
"I wanted to say that he was wrong. That it absolutely wasn't true that everyone was doping themselves. That I didn't do it. But I was stunned. I didn't say anything. I felt it was wrong to say anything."
The revelation prompted Anders Solheim, the head of Norway's anti-doping organization Anti-doping Norge, to express his disappointment.
"We think it would have been natural to take contact with the anti-doping organizations," said Solheim while noting the "omerta", or culture of silence within the sport at the time.
"There wasn't the climate for whistle blowing in 2011 that there is in 2014, said Solheim. "That you don't say what you know about doping. That's a challenge for anti-doping work within the sport."
The 36-year-old Hushovd defended keeping the admission to himself, saying he did not want to join in the media circus surrounding Armstrong.
"Many will surely claim that I all but defended Lance," Hushovd wrote. "I had no need to convict him. Why should I hop onto the wave and blast Armstrong because circumstances and the media expected that?"
Hushovd also wrote that he believed the International Cycling Union (UCI) covered up doping positives to protect the sport.
"I believe the system was corrupt. Lance was the great superstar and the golden calf of the sport. For UCI it would be a great loss if Armstrong was caught and revealed as a cheat.
"I believe that positive tests were hidden away in order to save Armstrong and to protect the sport of cycling."
A press conference to launch the book is planned for Thursday in Norway.