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."
Walcott also expects Welbeck to be very much at home in his new surroundings in no time at all.
“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."
