In the event of a Brexit according to the negotiated Withdrawal Agreement, free movement will continue as before until the end of the transition period on 31 December 2020.
In the event of a “crash-out” Brexit, the EU plans that UK citizens travelling to Germany and other countries in the “Schengen area” should be granted visa-free travel for 90 days in any 180 days.
The European Council has stated: “According to EU rules, visa exemption is granted on the condition of reciprocity. The government of the United Kingdom has stated that it does not intend to require a visa from EU citizens travelling to the UK for short stays.
In the event that the United Kingdom introduces a visa requirement for nationals of at least one member state in the future, the existing reciprocity mechanism would apply and the three institutions and the member states would commit to act without delay in applying the mechanism.”
Negotiations on this plan with the European Parliament are ongoing.
Further information can be found on the website of the European Commission: Visa free travel after Brexit: Council agrees negotiating mandate
After a “crash-out” Brexit British citizens would no longer be able to use e-gates. Britons would be third country nationals and would not enjoy the same privileges EU citizens enjoy at the border. British citizens would have to prove the purpose of their visit to Germany and their ability to cover all their expenses during their visit. Therefore it would be advisable to carry relevant documents with you and to allow more time for border controls than before Brexit.
British citizens who wish to move to Germany after a “crash-out” Brexit would be allowed to enter without a visa, live and work for a maximum period of 3 months. Within this period they would have to apply for a residence and work permit with the relevant foreigners authority.