The 19-year-old joined Celtic in 2018 after turning down a college scholarship from the University of California at Los Angeles (UCLA) but made just one appearance for the Hoops, starting the 1-1 draw with Hibs in January after 13 first-team players were forced to miss the match through self-isolation.
Harper has signed a three-year deal with the Harrison-based club, with the option of an additional year.
Red Bulls Head of Sport Kevin Thelwell said: “We are delighted to welcome Cameron to our club.
“Cameron is a sharp young talent who has been rising through the ranks of Celtic and the U.S. Youth National Teams.
"He possesses mental, physical, and technical attributes that make us believe he has a bright future, and we’re pleased that he has decided to take the next step in his career with us.”
Coach Gerhard Struber added: “Cameron is an exciting attacking player, with athleticism and strong technical ability. As a staff we are excited to work with him and help him continue to develop his game.”
Speaking to Celtic’s website Harper said: “I have really enjoyed my time at Celtic, it has been a great experience, of course I’m very grateful for the offer made to me by Celtic too, but I wanted to go back to the US and take this new opportunity.
"Of course, it goes without saying, I wish Celtic nothing but success for the future.”
A spokesperson for the club said: “Cameron leaves with the best wishes of everyone at the club.”