The 23-year-old Colombian, who joined the Hornets five years ago, has agreed a contract until 2025.
"In the EFL, you can name no more than 11 non-homegrown players on your matchday team sheet, so this is an important part of our thinking when it comes to player trading during this summer window," said Giaretta.
"Rob was clear he wanted a different type of player who will occupy this non-homegrown place in the forward line."
The exact amount paid by Columbus, who are currently 11th in the MLS Eastern Conference, has not been disclosed.
"Despite being just 23 years of age, he has shown a nose for goal against top level European opposition, and we firmly believe that he will flourish in our league," said head coach Caleb Porter.
"This investment is a testament to the belief our ownership group has in this club and our commitment to championship ambitions year in and year out.
"We believe he can be that consistent goal scorer we've been looking for to turn our positive play into more consistent results."