The Tour de France winner called on the American to come clean to prevent any further damage to cycling's reputation.
"Everyone knows he's a stubborn man. He has too much to lose, but the evidence speaks for itself. [It] looks overwhelming," BBC Sport quotes Wiggins as saying.
"There's a lot of anger. It's a shame cycling has being dragged through this again. It had to come out.
"Us riders here now - and I think I speak for all of us - we're the ones picking the pieces up and having to convince people the sport has changed."
Armstrong was banned from cycling and stripped of his seven Tour de France titles after the United States Anti-Doping Agency released a report that accused him of being involved in "the most sophisticated doping programme he sport has ever seen".