Media reports said Arsenal paid £34.5 million ($45.5 million) plus add-ons to sign the 24-year-old Ecuador international on a five-year deal.
Hincapie, who is currently at the World Cup, made 25 league appearances last season as Arsenal lifted the English top-flight title for the first time in 22 years.
He had also prominently featured in Leverkusen's Bundesliga campaign in 2023-24, when they won the German league unbeaten.
Hincapie, who started in Ecuador's first two Group E matches, is expected to play against Germany later on Thursday.