The visit, at the request of the Foreign Office, comes a few months after Britain is due to start the formal process for leaving the the European Union.
Britain is set to trigger two years of divorce talks with the EU by the end of this month.
The Duke and Duchess of Cambridge are stepping up their royal duties on behalf of William's grandmother Queen Elizabeth II, who turns 91 in April.
The couple are already due to visit Paris later this month.
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Queen Elizabeth paid a state visit to Germany in June 2015. She and her husband Prince Philip visited the Bergen-Belsen concentration camp to mark the 70th anniversary of its liberation by British forces.
William travelled to Germany last year, visiting Dusseldorf for a series of events honouring the role of British armed forces based in the country.
Kensington Palace said full details of the visit would be released at a later date.