According to L’Equipe, the Bundesliga club will pay an initial €23 million, with an additional €2 million in performance-related bonuses.
Medina has already agreed personal terms with Leverkusen and is expected to sign a five-year contract once he returns from his holiday.
The German side increased their offer after an initial bid was rejected by Marseille, eventually securing an agreement.
The transfer provides Marseille with a significant financial boost as they continue reshaping their squad ahead of the new season.
Medina joined the French club only last year after impressing during his spell at RC Lens. His departure marks another major change for Marseille, who are also reportedly close to selling goalkeeper Geronimo Rulli to Manchester City this summer.