There was uncertainty about Rooney's future during the summer after outgoing manager Sir Alex Ferguson revealed at the end of last term that he had asked for a transfer, and Chelsea were interested in signing him.
However, United always insisted he was not for sale and the striker has kept his focus on performing as well as possible.
The fans have continued to give Rooney their backing and he was particularly moved by the ovation he received as he was substituted against Bayer Leverkusen on Tuesday night, having netted twice to reach the landmark of 200 goals for the club.
"The reception I got when I was substituted was amazing and meant a lot so I want to thank the fans for that," he told his official website.
"The Manchester United fans have been brilliant since the start of the season, their support home and away is always top drawer and means a lot to the team. The best way to repay the fans is with good team performances.
"I'm happy to be in a position where I get the opportunity to score goals - and long may that continue."
Rooney's double against Leverkusen made him only the fourth player to score 200 goals for United, and he is delighted to be part of such an exclusive club.
He said: "It's a great honour for me to have scored 200 goals for a club like Manchester United.
"When you look at the list of top scorers I think I'm only the fourth player in the club's history to have reached this number after Sir Bobby Charlton, Denis Law and Jack Rowley. It's certainly something I'm very proud of.
"My main aim is always to help the team win games and if I score that's a bonus. Hopefully there are still a few more goals to come from me yet."
Rooney is already looking forward to United's next challenge, a derby game away to Manchester City on Sunday, and he is anticipating a tough game.
"My main focus now is preparing as well as possible for the game against City at the weekend," said Rooney.
"We all know they are a strong outfit and have made some good signings over the summer so we will definitely need to be at our best come Sunday."
United manager David Moyes paid tribute to Rooney's performance after the Champions League victory over Leverkusen, labelling the striker 'world class' after he also set up Antonio Valencia.
Moyes said: "Wayne played really well tonight. He scored his goals and his pass to put Antonio in was terrific.
"We want him to keep that scoring record up. I think there are only three or four Manchester United players that have ever achieved 200 goals.
"I remember saying that he could go on to become one of the all-time greats here by his goals.
"I thought his performance tonight was excellent. I think everything he did was worthy of two goals, and maybe more.
"I think you can see from the way he was moving that he's in a good place at the moment and any forward who's scoring goals feels good about himself.
"Any team that wants to win the Champions League needs to have several world class players - and Wayne would certainly come into that category."