The Costa Rica international joined Arsenal in 2011, but has spent the past three years out on loan at Lorient, Real Betis and Olympiakos.
He made his first appearance for Arsenal as a late substitute in last weekend’s Community Shield win over Manchester City and is in contention to feature in Saturday’s opening Premier League game at home to Crystal Palace.
Campbell, who impressed during Costa Rica’s run to the World Cup quarter-finals, is happy that he will be part of Wenger’s plans this season.
“I’ve always dreamed of playing for Arsenal since I was a young kid watching Thierry Henry,” the forward told The Sun.
“The manager has told me he wants me to be part of his plans and not send me on loan again. Now I want to repay his faith.
“I’ve no doubt I can succeed as I’ve now played more than 100 matches and got 36 caps for my country, and played in the world’s biggest tournament.
“So playing in the Premier League holds no fear, only excitement.”
Arsenal manager Wenger is pleased with Campbell’s development and confirmed he is not currently looking to send him out on loan.
"He has come from a non-competitive world to a world with hyper-competition," Wenger said.
"He has adapted slowly, but has adapted very well, he has a very good spirit and attitude.
"He is a member of my squad at the moment, He had a good preparation and played well against Benfica.
"In training he is very focused and eager to do well. I would like to keep him."