Welbeck completed his move to the Emirates Stadium from Manchester United on transfer deadline day last week for a reported fee of around £16 million.
The Manchester-born 23-year-old is a graduate of United's youth system, but struggled to establish himself as a first-team regular at Old Trafford after making his debut in September 2008.
Welbeck was England's match-winner in their opening Euro 2016 qualifier on Monday, scoring both goals in a 2-0 win in Switzerland after starting in his favoured centre-forward position.
And Owen, who played with Welbeck at United, expects his former team-mate to go from strength to strength under the tutelage of Arsenal boss Arsene Wenger.
"He has always had doubters, but I have always been a big fan of Danny's," Owen said.
"I trained with him for three years [in] my time at Manchester United and he is a player - he can play, no question about it.
"People will complain about his goals ratio for Manchester United, but you try getting in the side.
"I had a go trying at centre-forward with Robin van Persie, Wayne Rooney, Chicharito [Javier Hernandez] - there are so many good players at United.
"And a lot of the time when Danny did play, he would play out on the left or out on the right and different positions.
"As his England career would suggest, when he plays down the middle he can certainly score a goal and I think he is a pretty good buy for Arsenal."
Welbeck is in line to make his Arsenal debut when his new club host Premier League champions Manchester City on Saturday.
