Welbeck joined the London club from Premier League rivals Manchester United in a reported £16 million move just ahead of the transfer deadline.
The 23-year-old England international failed to nail down a regular starting berth at Old Trafford and was deemed surplus to requirements following the arrival of Radamel Falcao on loan from Monaco.
Welbeck scored both goals in England's 2-0 Euro 2016 qualifying victory over Switzerland on Monday and Arsenal forward Walcott knows all about the qualities he possesses, having played alongside him at international level.
Walcott, currently sidelined with a knee injury, has backed Welbeck to be a big hit at the Emirates Stadium and wants to see Arsene Wenger's new recruit be more ruthless in order to become a more regular goalscorer.
The former Southampton man told Arsenal Player: "I've worked with Danny for England and we link up very well.
"He’s another English guy and we've got a good English core now.
"He's going to be better for us than he was at Man United, definitely. He'll get more opportunities and he's got a point to prove. I know he's worked hard and he's still very young, and I think the boss will enjoy working with him.
"The fans definitely will - he's very exciting and he's very strong.
"One thing I would tell him to do is be a little more selfish because he's unselfish at times, which isn't a bad thing but I think he'll get more goals if he's more selfish. I'm sure he'll do well for us."
“He's a very good guy and a very hard worker," he added.
"Off the pitch he's very relaxed and likes to get involved in anything. He's just a very well-spoken young man and he's always eager to improve and spend time with people.
"He fits perfectly into Arsenal, which is such a big family club where everyone's together. He'll fit straight in here."
