The England international signed for the Gunners on transfer deadline day for around £16m, and Walcott feels that the ex-United forward can become more complete footballer if he learns to be more "selfish" in front of goal.
Walcott told the club's official website: "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 Manchester 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."
Welbeck scored both goals in England's 2-0 win over Switzerland on Monday evening.