The 31-year old completed the move from Manchester United on Sunday.
"Ronald Koeman was very influential in me coming here," Rooney told the club's website.
"When it was obvious I was going to be leaving Manchester United this summer, Ronald came out a few times and said how much he wanted me at the Club and that had a huge impact on me.
"There were other options there but once I knew that Everton wanted me to come back then it was the only option for me.
"Bill obviously played a big role in it but the important one was Ronald Koeman.
"He was the one who picks the team and he's the one who has his ideas on the football pitch.
"There were a lot more things behind the scenes which needed to happen but, for me, the important person to speak to was Ronald Koeman.
"As I spoke to Ronald and saw it in his eyes that he wanted me to be part of his team, it was a no-brainer for me and the only place I was going to go."