"We've agreed the purchase of Zapata," the Serie A club's president Aurelio De Laurentiis said on his Twitter feed on Friday. "The player is on his way to Naples for the medical."
The 22-year-old, who began his career at Colombia's America, scored 13 goals in the Argentine first division last season.
Zapata is set to join a Napoli squad that contains several other new signings including Argentina striker Gonzalo Higuain.
Napoli, runners-up to Juventus in Serie A last term, open the season at home to Bologna on Sunday (1845 GMT).