Since arriving at Leverkusen in 2021, the 23-year-old has racked up over 100 appearances and was instrumental in their 2024 Bundesliga title triumph.
British media reported that Arsenal have a 45 million pounds ($60.79 million) agreement in place to buy Hincapie if they decide to make his move permanent next summer.
"Piero has a real physical presence, with his versatility and tactical flexibility giving us strong added defensive options," Arsenal manager Mikel Arteta said.
"He is a big character, with a very good combination of both youth and maturity. He will make our squad stronger and more competitive as we continue into this season."
Piero will take the number five shirt and link up with his new teammates once he returns from international duty.