Already Van Persie has had a positive impact, scoring eight times in his first 11 appearances, including a memorable hat-trick at Southampton in August.
But Van der Sar is confident there is much more to come from the 29-year-old, and he said: "I am glad Van Persie is there It is always nice when someone like that decides to go to the club."
He continued: "I spoke to him about it and I know it is the right place for him. He can really add something to the team.
"It was difficult for him at first because he didn't know if he was running into the right areas. But he has settled in very well.
"He is a great guy to have around. He works so hard on and off the pitch.
"I know there has been a focus on youth at United but he will improve the team."
The Red Devils have not won a domestic game at Stamford Bridge since 2002 and despite Chelsea's surprise defeat at Shakhtar Donetsk on Tuesday, Van der Sar is not expecting it to be any easier this time around.
"We didn't win at Chelsea too many times when I was at United and it won't be any easier this weekend," he said. "They have changed their formation. They are more lively now and have more go-forward in their team. They certainly look to have great attacking options in midfield, which is the area United seem to have struggled a little bit."