The French forward has put pen to paper on a five-year deal with the reigning Bundesliga champions.
Terrier is Xabi Alonso’s third signing ahead of the 2024-25 season, joining Jeanuel Belocian and Aleix Garcia at BayArena.
The 27-year-old scored 42 goals across his last three seasons with Rennes, despite missing nine months of action with an anterior cruciate ligament injury.
“It’s been my wish to move to a big club abroad in Europe after seven years as a professional in France,” he told the club’s official website.
“The fact I now get to show my skills with the German double winners is magnificent and a special motivation for me.
“Bayer 04 also made headlines in France with their achievements last season. It’s fantastic to be a part of this team from now on.”
“In Martin Terrier, we’ve gained a prolific, fast and intelligent forward,” Leverkusen’s managing director for sport, Simon Rolfes added.
“Martin is a strong finisher and versatile – a good footballer who fits into our team superbly with his profile. We’re delighted he’s decided to join us