Agudelo came up through the Red Bull Academy and made his first-team debut in 2010. He was stuck behind Thierry Henry and Kenny Cooper, who are tied for second in Major League Soccer with nine goals each.
"He thought his chances to develop as a player would maybe get better ... if he played somewhere else," Red Bulls general manager Erik Soler said. "Out of respect for Juan, we decided to give him this chance."
Agudelo is the latest young American player to leave New York, following goalkeeper Tim Howard, forward Jozy Altidore and defender Tim Ream. New York turned down offers from foreign clubs for Agudelo.
"We're still a small league," Soler said. "We are still not at the top of the pyramid."
Chivas USA replaced Pearce by obtaining defender Danny Califf from Philadelphia Union for midfielder Michael Lahoud and allocation money.
Agudelo, 19, made his U.S. national team debut in 2010 and has two goals in 15 international appearances. He failed to become a regular with the Red Bulls last year and missed the start of the MLS season after tearing knee cartilage while playing for the U.S. under-23 team that was eliminated in Olympic qualifying.
He won't be away from Red Bull Arena for long: Chivas USA visits on Wednesday.
The 27-year-old Pearce can play defender or midfielder and joins a Red Bulls team that has yielded a league-high 23 goals in 11 games. He was among the final cuts from the 2010 U.S. World Cup roster. Pearce played previously with Denmark's Nordsjaelland (2005-07). Germany's Hansa Rostock (2007-9) and FC Dallas (2009-10).
Califf, 32, signed with Philadelphia in 2010 after he played in Denmark for AaB Aalborg and Midtjylland.