The 20-year old forward, who only joined the Goats from New York Red Bull in May last year, has returned to the East Coast with the Revs picking him up in exchange for allocation money.
"We're very pleased we were able to complete this deal with Chivas USA," Revolution GM Michael Burns said in a statement.
"While Juan is a young player with tremendous potential, he also already has a lot of experience both inside our league and internationally with the US national team. We believe Juan will improve our attack and make us a better team."
In 59 MLS appearances, including 33 starts, for both New York and Chivas, Agudelo has scored 11 goals and provided six assists.