The 18-year-old was part of Barcelona's youth system before moving to New York. He scored on his first-team debut last October and has made eight appearances in 2020-21, managing four goals and an assist.
"Caden Clark has fantastic skills and enormous potential," Leipzig technical director Christopher Vivell said. "He can play anywhere across attacking midfield and is incredibly adaptable in his playing style.
"As well as that, he is a scoring threat, has great passing quality and strikes the ball well, allowing him to score goals from range.
"These skills make him a perfect fit for our playing philosophy."
Clark's move has long been rumored, considering the connection between the clubs.
He scored six goals in the previous MLS campaign including playoff appearances, despite spending just 770 minutes on the pitch.
His form has been impressive in 2021, too, though Clark – who is yet to play for the United States but was recently included in the national team's preliminary squad for the 2021 Gold Cup – is currently out of action after undergoing an appendectomy.
"I am extremely grateful for the opportunities that the New York Red Bulls have given me," the talented prospect said in a statement.
"Being able to not only develop but play significant minutes at USL and MLS here has truly helped me grow professionally. I will continue to do what I can to help this team win its first MLS Cup."