Rooney completed his move back to his boyhood club after a 13-year absence on Sunday, leaving Old Trafford as United's all-time leading goalscorer.
Bolasie believes that the 31-year-old is still a "world-class" player and is confident that the new arrivals - of which there have been six so far - can help to limit the impact of losing Romelu Lukaku to Manchester United.
"I'm itching to get the shirt on. There are some top quality players that have come in, especially Rooney, who is world class. He will bring a leader's mentality and it will be good to learn off him," he told talkSPORT.
"The signings we have made have definitely made the team stronger. The competition for places is going to be strong, but that is what I live for and I am looking forward to fighting for my place. It will bring another level to my game.
"At Everton we have made some great signings that can cover Rom's goals in all different types of ways. We just have to move on and we look forward to the future because the future for us is exciting."
Bolasie is currently with the Everton squad on their pre-season trip to Tanzania.