The illegal drugs were discovered two weeks ago in a Netherlands-bound shipping container from Uruguay during a search in the northern port city of Hamburg, they said.
When customs agents opened the container, which according to the manifesto was loaded with soybeans, they found more than 200 sports bags packed with over 4,200 packages of compressed cocaine.
The 4.5 tonnes surpassed total seizures of 3.8 tonnes made in Hamburg in 2017.
"This enormous quantity represents the largest single seizure of cocaine in Germany," said the customs service in a statement.
"Assuming that this probably very pure cocaine can be diluted to triple the amount for street sale, the 4.5 tonnes have a street value of approximately one billion euros."
The service said that "the cocaine seized has already been destroyed in secret and under extensive security precautions".