Rooney, speaking ahead of England's friendly with Norway at Wembley on Wednesday, was unmoved by suggestions Falcao's arrival could jeopardise his position in the starting XI at Old Trafford.
The England and Manchester United captain said: "I obviously don't know how Falcao's arrival could affect my role, that's something you'll have to ask Louis van Gaal.
"I think it is a fantastic signing. He is one of the best players in the world. It is a real show of intent by Manchester United.
"It is a thrill. We have an exciting team. I am looking forward to the challenges ahead and I want it to be successful."
United confirmed the arrival of Falcao from Monaco on an initial season-long loan with an option to buy in the early hours of Tuesday morning.
This came after the club applied for an extension past the 11pm deadline to ensure the necessary documents were correctly filed with the Premier League, thus ensuring the deal would go through.
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