Neil MacGregor, who has been in charge since 2002, will leave in December to work on part-time projects including advising German Culture Minister Monika Grütters on the development of the Humboldt Forum.
MacGregor organised a popular exhibition on German history last year at the British Museum, which is the most visited tourist attraction in Britain – and even drew a visit from Chancellor Angela Merkel.
It was also the subject of an acclaimed BBC radio series and an accompanying book.
The Humboldt Forum, a new museum due to open in 2019, is described by Grütters as "our most ambitious cultural project" and will be housed in a rebuilt former imperial palace in central Berlin.
"The Humboldt- Forum, drawing on the outstanding resources of the Berlin collections, can become a place where different narratives of world cultures can be explored and debated," MacGregor said.
Media reports suggest that MacGregor could eventually be a candidate to run it.
After leaving the British Museum, he will also work alongside the CSMVS Museum in Mumbai – India's most prestigious – and on a new series for BBC radio.
During his time at the British Museum, MacGregor defended its right to keep its most controversial artefacts, the Elgin Marbles.
The museum's loan of part of the Elgin Marbles to the Hermitage Museum in St Petersburg last year drew an angry response from Greece, which wants the return of the sculptures which were once part of the Parthenon temple on the Acropolis in Athens.