The restrictions, which also applied to people from Portugal, Russia, India and Nepal, will be relaxed from Wednesday.
Visitors who are fully vaccinated will also not be required to quarantine.
Non-vaccinated people will however still be required to quarantine for up to 10 days, with the option to end their quarantine early with a negative test on the fifth day.
The five countries have until now been classified as "virus variant areas" because of the spread of the Delta and Delta Plus variants, which were first identified in India.
Although German citizens and residents were exempt from the ban, they were required to quarantine for 14 days when they arrived in the country.
The countries will now be reclassified as "high incidence areas", the Robert Koch Institute (RKI) said on Monday.
Germany's relaxation of restrictions came a few hours after UK Prime Minister Boris Johnson confirmed the country is expecting to lift all Covid-related rules from 19 July.
The UK government is also expected to announce plans for fully-vaccinated British people to travel to "amber" countries - that is, countries designated as medium risk for Covid, including many in Europe - without having to quarantine on their return.
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