The 30-year-old lodged an appeal after his initial application was rejected but when the appeal failed, it was agreed to end his contract.
"After going through the entire immigration and appeals process, Luke's P-1 Visa application has unfortunately been denied by the U.S. government for now," the Red Bulls said in a statement.
"We have spoken with Luke about potential options and have mutually decided that it would be in all parties' best interests to terminate his current MLS contract so he could play elsewhere."
Rodgers, who played in England for lower league clubs Shrewsbury Town, Port Vale and Notts County, scored nine goals in 20 regular season starts for New York, where he played alongside former Arsenal and France striker Thierry Henry.
New York said they remained open to a possible return should they find a solution to the visa problem.
"We will also continue to track his progress this year while working with immigration officials with the goal that he could join the Red Bulls sometime in the future," the club said.
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