The 24-year-old leaves TFC after three seasons and 92 appearances across all competitions. The Red Bulls sent their natural fourth round pick in the 2017 draft to Toronto.
A 24-year-old right back who can also fill in elsewhere along the backline, Eckersley joined Toronto on loan from Burnley in England ahead of the 2011 season. His popularity with fans and coaching staff led to a permanent deal being reach that kept Eckersely with TFC for the 2012 and '13 campaigns.
“Moving someone that has been with the club for an extended period is always a difficult decision," TFC general manager Tim Bezbatchenko said in a statement. "However with the acquisitions we made during the off-season particularly in defence; along [with] the cap relief, this move made sense.
“We’d like to thank Richard for his contributions to the club over the past three seasons and wish him all the best in New York.”
Having appeared in 92 matches across all competitions for Toronto, Eckersley leaves TFC with the third-highest appearance total in club history. He is expected to compete with Kosuke Kimura for the starting spot on the right side of New York's backline.
“We were impressed with Richard’s play at Toronto FC and are delighted to acquire him," Red Bulls Sporting Director Andy Roxburgh said. "He has a good soccer brain and is an energetic defender who can also provide positive attacking qualities on the flanks.
“Richard will immediately provide another solid and versatile option for us on our backline and will certainly compete for a starting role on our team.”