Tillman, whose 33 goal involvements helped PSV win back-to-back Eredivisie titles in 2023/24 and 2024/25, has signed a five-year contract at the BayArena.
The 23-year-old attacker's arrival follows Florian Wirtz's transfer to defending English Premier League champions Liverpool on 20 June.
Tilman said upon joining Leverkusen: "This club has always played great football. In the last four or five years, Leverkusen have grown enormously and become attractive to a lot of players throughout Europe. I want to win something. That was my aim in Glasgow and in Eindhoven and it remains my aim here."
