The former Barcelona player was one of MLS's top earners last season, picking up $4.6 million, but he had a disappointing campaign and had a tense relationship with the team's fans.
"This decision has been made in the best interests of both parties concerned," Red Bulls sporting director Andy Roxburgh said in a statement.
"Rafa has accomplished a great deal during his career and is a top quality player. We want to think him for his service to the Red Bulls and wish him the best of luck."
The Red Bulls called the move a "mutual release agreement" with the 33-year-old, who still had a year left on his contract, but declined to give specific details.
Marquez was ultimately a disappointment as a 'Designated Player', operating under the so-called 'Beckham Rule' which allows teams to pay up to three players from outside the team's salary cap.
The Mexican's arrival, alongside former France striker Thierry Henry, was supposed to boost the club's popularity and help push them towards their first MLS title - but neither goal was achieved.
Shortly after the Red Bulls announcement, Mexican first division club Leon said Marquez would be presented officially to the team's fans on Friday at their home stadium.
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