The 24-year old German attacking midfielder joined the Gunners from Real Madrid on deadline day and former Chelsea and Bayern Munich ace Ballack is tipping him to bring all of his world class ability to North London.
"Mesut is a young player and at his peak," he said.
"He is an outstanding player, who joined a new club, I don't think it's a problem [being nervous about playing in England].
"Arsenal is a great club and paid a lot of money for him. That proves his exceptional standing on international level, this amount is not common.
"I really hope everything works well for him, he will be an addition to the league especially with his technical skills and pace with the ball."