The 20-year-old has signed with the Bundesliga club until June 2025.
He is Leverkusen's second Dutch signing this month after defender Timothy Fosu-Mensah joined from Manchester United.
Right-back Frimpong, a product of Manchester City's academy, will cover for Santiago Arias, who is sidelined by a long-term ankle injury.
Frimpong will miss Saturday's Bundesliga match at RB Leipzig due to a quarantine period after arriving from the UK.
He should first be available for next Tuesday's German Cup match against fourth-tier minnows Rot-Weiss Essen in the last 16.