The 23-year-old completed a deadline-day switch to the Gunners from Manchester United and is expected to make his debut for the club in this weekend's Premier League match against Manchester City.
"I've heard people say he is never going to be a 20 or 25-goals-a-season striker. I disagree," Shearer told BBC Sport. "He now has an opportunity to stamp his authority on the Premier League.
"It is not until you feel like the main man or part of a team that the confidence comes out. Once Welbeck gets in that Arsenal team and gets three or four goals, he can go on and get a load of goals."
Welbeck scored 29 goals in 142 appearances for Man United.