Cooper returns to Dallas where he scored 40 goals in 90 MLS appearances between 2006 and 2009 after netting 18 times in 33 outings for the Red Bulls in 2012.
"We're really excited to have Kenny Cooper back in Dallas," FC Dallas head coach Schellas Hyndman said in a statement.
"When I first became the coach at FC Dallas, Kenny was our striker. He is a proven goalscorer, a Dallas boy returning home to his roots. Kenny is a leader with exceptional character."
New York sporting director Andy Roxburgh said the trade was the something the club did hesitantly as they were keen to retain the services of Cooper.
"Due to salary cap restrictions and in order to balance our squad now and in the future, we have very reluctantly traded Kenny," Roxburgh said in a statement.
"The allocation money combined with the salary cap relief that we obtained will be vital for us to strengthen the squad in specific areas. Kenny, who is a great professional as well as an excellent person to work with, has been a very good member of our roster and we wish him every success with the next phase of his playing career."