On Friday the piece was put on display in Neil MacGregor's final act as director and has been made from the wreckage of a boat that sank off the island of Lampedusa in the Mediterranean sea.
It goes on display as Mr MacGregor leaves his post.
He told The Times that the Lampedusa Cross was created by a carpenter on the Italian island to commemorate the suffering of migrants fleeing conflict in African countries for Europe and to symbolise a key moment in human history.
Francesco Tuccio created the piece to express his frustration at not being able to help those on the sinking boat on October 3rd 2013, so he took wood from the vessel to make them gifts.
He discovered that of a number of the 151 people that survived were Christians from Eritrea, and decided to create a cross for each person.
This cross is made from the wreckage of a boat carrying Eritrean & Somalian refugees. One was given to each survivor pic.twitter.com/PEtVZRDVuE— British Museum (@britishmuseum) December 18, 2015
Mr Tuccio also created one for Pope Francis, who carried it at a memorial service for drowned migrants.
Mr MacGregor said: "This simple, yet moving object is a poignant gift to the collection."
"Mr Tuccio's generosity will allow all visitors to the museum to reflect this significant moment in the history of Europe, a great migration which may change the way we understand our continent.
"In my time at the museum we have acquired many wonderful objects, from the grand to the humble, but all have sought to shine a light on the needs and hopes of all that human beings share."
"All have enabled the museum to fulfill the purpose for which it was set up: to be a museum of the world and for the world, now and well into the future."