The former Manchester United captain completed a return to Goodison Park on Sunday, 13 years on from his move to Old Trafford as an 18-year-old.
Rooney insisted at his presentation that he was not moving “to a retirement home” and is determined to end Everton’s 22-year wait to win a major trophy.
And Koeman believes his drive to add more success to a glittering career could be an important lesson to the rest of the squad.
“Everybody knows the qualities of Wayne,” Koeman said. “He’s really a striker and players with that quality can play out of position. He can be a 10 behind the striker, a free role from the left, a nine, a seven.
“The qualities of the player are the most important. We like to win trophies and that’s a feeling that not all the players have at Everton. We have a lot of young players and that experience of winning titles is really important for Everton. It’s one of the reasons we tried to bring him back.
“When we spoke, it was about the ambition. He showed me that he likes the pressure. He’ll have pressure next season and he’s used to that.
“Some players need pressure to get the best out of themselves. He’s 32 in October and that’s still young for football. The ambition he showed was enough to convince me.
“I’d prefer to have 10 players scoring 10-15 goals than one scoring 25. Wayne is the kind of player who can bring productivity to the team.”
Everton have agreed a fee with United for striker Romelu Lukaku, reported to be £75million, and the Belgium international is expected to finalise his move in the coming days after passing a medical in Los Angeles.
Koeman bears no ill-will towards the 24-year-old and hopes he enjoys success at Old Trafford.
“We know it was one of the challenges for Lukaku,” he said. “He took the right decision and let’s hope everything will go well for him. I like him, but now it’s about Everton.”
Everton have been linked with a bid for Swansea City’s Gylfi Sigurdsson, while the future of Ross Barkley remains unclear, but Koeman would not discuss any other transfer business.
“We’re doing good business and we’ll see in the next weeks what more we’ll do. You know me, you can mention all the names, but I won’t respond about that,” he said.
“Everybody knows one really big reason to sign for Everton on year ago was about the project. The club is showing the ambition that everybody likes to have. It’s exciting times for Everton Football Club.”
Asked about Barkley’s future, he replied: “It’s a nice question for the next press conference.”
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