Van Persie completed his move from Arsenal to United on Friday and has already started training with his new teammates.
"It's great for the players and the fans to sign a player of Robin's quality," he said. "The two of us were fighting for that Golden Boot last season and now the two of us are hopefully playing together.
"Obviously we'll have to work over the next few weeks and try to develop an understanding. Hopefully it will come quite quickly and we can form a good partnership.
"I haven't thought about how my role will change. I only trained with him on Friday for the first time. No matter what role the manager wants me or Robin to play we will have to do that."
Rooney also believes that 29-year-old Van Persie will help ease the burden of scoring goals on him.
"I know over the last two or three years I've been the one scoring the goals," explained the 26-year-old. "But you can't do that without the players to give you the assists.
"For me, there are still high expectations and I set them for myself. The only thing that might change is that we might be able to share the goals out a little more.
United will begin their Premier League campaign with an away game against Everton on Monday.