The 26-year-old Portugal international put pen to paper on the new deal last Thursday.
"I'm very happy," he told MUTV. "It's always a pleasure to be at this club and be part of the great teams all these years. I'm so proud to sign a new deal with Manchester United because that's what I wanted to do.
"At the moment, I'm more relaxed to just focus on football and concentrate on what I want to do - to help the team and be at my best.
"Since I started my professional football career, the most part was here - all the successful seasons were here at Manchester United. I feel at home. I feel good at this club because this club can give you a lot of things. I'm so happy to be here."
Nani joined United from Sporting Lisbon in 2007.