Red Bull, who brought in French forward Thierry Henry last month, said they had signed Marquez to a multi-year contract as the club's third 'designated player'.
Colombian Juan Pablo Angel and Henry are the other two players whose salaries are mostly outside the team's salary cap.
Marquez, a defender who can also operate in midfield, has spent the past seven years with Spanish club Barcelona and previously played for French club Monaco.
The 31-year-old was released from his contract with Barcelona on Saturday, paving the way for his move to the States.
"Rafael has shown on the club and international level that he is one of the world's top players," Dietmar Beiersdorfer, head of Red Bull Global Soccer, said in a statement.
"He has been a winner at all levels and illustrated that he is a leader both on and off the field. We are thrilled that he decided to come to the Red Bulls at this time in his career."
Marquez, who had been linked with several European clubs said he was delighted with the move.
"Coming to New York and playing in Major League Soccer was a chance that I could not refuse. I am committed to doing my very best to help the Red Bulls in their play-off push this year and compete for championships in the years to come," he said.
Marquez, who has played 94 times for Mexico and has been skipper since the 2002 World Cup, will be unveiled to the media at a news conference on Tuesday.
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