Andrich, 29, arrived at the club from Union Berlin in 2021 and has since gone on to play 118 times for Leverkusen, scoring 16 times.
The midfielder made his Germany debut last November and has since played 10 games for the national side, including every match of the team's run to the Euro 2024 quarter-finals.
Last season, Leverkusen became the first side in Bundesliga history to go through a season unbeaten, winning their first top-flight title while adding the German Cup.
In a statement, Andrich said Leverkusen was "absolutely the right address.
"I am experiencing the most successful period of my career and I feel that the team's hunger is still great even after this special season."
Leverkusen sporting director Simon Rolfes called Andrich a "central pillar" of the club while praising his "outstanding performances on the international stage".
Leverkusen open their season in Saturday's German Super Cup, hosting Stuttgart.
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