"I have not come here to finish my career; I am only 31 years old," the Mexico captain told reporters. "I have come to play and to win championships."
Marquez's arrival in New York completes a hat-trick of big-name signings by the Red Bulls. He will line up alongside Colombian Juan Pablo Angel and French forward Thierry Henry, who joined the team last month.
After spending the last seven years with Spanish club Barcelona operating mostly as defender, Marquez will move up to play a central midfield role but Red Bulls coach Hans Backe provided no timetable for his Major League Soccer debut.
"He will definitely be in central midfield with his distribution and his knowledge of the game and his vision, so definitely central midfield," said Backe. "Today we bring in experience, leadership and I could say quality, on the pitch.
"He will definitely make a difference on our midfield so I'm really a happy man today. About his shape, I have to talk to Rafael.
"He had his first session today after being on vacation after the World Cup so we haven't decided when he can play so far."
(Writing by Steve Keating in Toronto; Editing by Sonia Oxley)