Reuters reports, citing a government source on the matter
The source says that the German cabinet has approved plans today to allow for people who have been fully-vaccinated against COVID-19 or recovered from the disease to enter the country without having to undergo the quarantine procedure.
Adding that this will not apply to those coming from high risk areas though, while the vaccine has to be one that is approved by the EU i.e. Pfizer, AZ, Moderna, J&J.
This somewhat ties back to the proposal made by the EU earlier in the month here and is also surely a step that most countries in the region will begin to take before the summer travel season approaches in the months ahead.