Welbeck, 23, joined the Gunners from Manchester United for £16m on transfer deadline day, and could make his debut against Manchester City on Saturday.
“I’ve heard people say he is never going to be a 20 or 25-goals-a-season striker. I disagree,” Shearer told BBC Radio 5 live.
“He now has an opportunity to stamp his authority on the Premier League.”
On Thursday, Manchester United manager Louis van Gaal said Welbeckdid not score enough goals during his time at Old Trafford.
The Manchester-born forward, who netted both of England’s goals in the2-0 win in Switzerland on Monday, has not managed more than nine goals in a Premier League season since making his senior debut in 2008.
He struggled to hold down a regular place in the United starting line-up, particularly in his favoured role as a central striker, and his chances would have been limited further by the arrival of Radamel Falcao.
Louis van Gaal said Danny Welbeck did not match the goal-scoring standard of Robin van Persie and Wayne Rooney
After joining Arsenal, Welbeck said he hoped to get the opportunity to play in a centre-forward role.
BBC Sport pundit Shearer, who came through the youth ranks at Southampton before joining Blackburn Rovers in 1992, feels Welbeck has made the right decision to swap Old Trafford for Emirates Stadium.
“When I left Southampton at nearly 22, I was not a regular goalscorer,” said Shearer. “I scored a hat-trick on my debut and then found goals quite hard to come by.
“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.”
Shearer likened Welbeck’s situation to that of Thierry Henry when he signed for Arsenal from Juventus in 1999.
The former France international had played predominately as a winger prior to joining the Gunners, but played as a striker under Arsene Wenger, scoring 228 goals in 377 appearances.
Arsenal move
“I am not putting him in the bracket of a Thierry Henry, but look at what Arsene Wenger did for him,” added Shearer.
“He was not a centre-forward, he was struggling for goals and confidence and look what happened there.”
Former Liverpool striker Emile Heskey echoed Shearer’s belief that Welbeck can thrive at Arsenal, and expressed surprise he was allowed to leave Old Trafford.
“If you look at the players United have, he would have given them something different with the pace he has,” said Heskey.
“If you go through the stats like Louis van Gaal has said, then you know why he has weighed it up that way, but I think he will be a great addition for Arsenal.”
