The Blues made a strong start to the season with a draw against Tottenham Hotspur.
The Dutchman took charge at Goodison Park this summer following the sacking of Roberto Martinez at the end of last season.
They made a positive start last week as they secured a draw against Tottenham Hotspur on the opening day of the season.
There was a noticeable difference in their style, as the first half saw them pressing high up the pitch and dominating Spurs for those 45 minutes.
Tottenham's Kyle Walker in action with Everton's Gareth Barry
And Campbell believes that Koeman will be making the Toffees more aggressive, adding that the signing of Yannick Bolasie shows they mean business.
“I think Everton are going to be a lot more aggressive,” he told Sky Sports.
“There was an issue last season because the team were passive. At Goodison Park it is like a fortress and the fans want the players to be aggressive. The Bolasie signing shows they mean business.”
Tottenham's Victor Wanyama in action with Everton's Ross Barkley
It remains to be seen just how Everton do under Ronald Koeman’s guidance this season.
The game against Spurs was a very clear indication of the way he wants them to play, with they high-pressing, high-tempo game on show from the start.
If they can perform as they did in those first 45 minutes for the rest of the campaign, then the Blues could be set for an exciting season.
Everton manager Ronald Koeman applauds fans after the game