Van Persie, 29, is the Premier League's top scorer after finding the net 18 times since moving from Arsenal last summer and doubts over his ability to back up last season's efforts were quickly allayed with four goals in his opening three games at United.
The Netherlands international, who is expected to line up for his country in Wednesday's friendly with Italy, says the quality of his team-mates and the advice of United coach Rene Meulensteen has helped him take his game to another level.
"It's gone as well as I've expected it to go," he said. "I go into work every day whistling, as from the first day they've made me feel welcome.
"The boys made me feel right at home. Training is really good and I see things I've not seen in a long time. It is a very pleasant environment to work in. Every day I work on new things. I have become alert to small details that make me better.
"The way he [Meulensteen] trains is refreshing. He is truly one of the best coaches in the world. I've had a lot of good trainers, but it's the way he prepares our team for games. Every match is different so every training session in build-up is unique. We know exactly what to expect. He wins points for us through his training.
"We've won a lot of games by the odd goal - they are point winners. Consider the game against Chelsea. I scored after a low cross from Antonio Valencia on the right. It might seem like a fluke, but the whole week before the game was spent working on that move. Another example is my goal against Wigan when I cut the ball inside and shot with my right foot - again this was a situation we trained on."
Van Persie's successful Arsenal career was hampered by a string of injury concerns and the Dutchman believes consistent football at United is aiding his fitness.
"This run of games without getting injured has only made me stronger," he said. "But I don't want to talk about it, touch wood. I feel better and fitter. Really fit. In the last week I played Wednesday and Saturday. In those games I played with ease. I feel fit and recover quickly as lightning."
United's Champions League round of 16 tie against Real Madrid will be van Persie's second meeting with the Spanish giants after Arsenal's 1-0 win at the Emirates in 2008.
"The match against Madrid is the icing on the cake for every footballer," he added. "It will be my first game at the Bernabeu - and I'm really looking forward to it. It will be a very nice challenge with the group of players we have.
"Manchester United are a big club and being in the last 16 is already beautiful even without the prospect of playing Real Madrid."