The 19-year old ballad singer, whose voice drew comparisons to Whitney Houston and Mariah Carey, beat runner-up Josh Krajcik to land a $5m (£3.1m) recording contract.
Amaro will also take a starring role in a new advertisement for Pepsi.
She had been tipped to win after an impressive rendition of Beyonce's hit "Listen" in Wednesday's live show.
Last night, she dropped to her knees and wept with joy, speechless at her victory.
A delighted Simon Cowell said the Amero was a worthy winner.
"We came here to find a superstar and we found a superstar," he said.
Second-placed Krajcik, 30, a bluesy rock singer who worked in a burrito restaurant before joining the show, also congratulated Amaro.
"Melanie deserves it. She has a wonderful voice", he said.
Recovering drug addict and rapper, Chris Rene, came third in the Christmas-themed, two-hour finale, which also saw performances by Justin Bieber, Stevie Wonder, Leona Lewis and 50 Cent.
Ratings for the show have fallen short of expectations, drawing an average of 12 million viewers - about half the audience for "American Idol".