The papers had been held by sisters Eva Hoffe and Ruth Wiesler, who argued they had legally inherited them from their mother, Esther Hoffe.
She was secretary to Kafka's friend, biographer and executor Max Brod, who ignored the German-language author's dying wish to burn all his unpublished work.
The archive includes three draft versions of Kafka's story "Wedding Preparations in the Country", an exercise book in which he practiced Hebrew, hundreds of personal letters to Brod and other friends and travel journals.
Since 2008, the library has won a series of legal rulings granting it possession of the documents, in accordance with instructions in a will written by Brod, who died in 1968.
The library said that since court proceedings ended in 2016, it has been collecting the papers from sites in Israel and Germany and, finally two weeks ago, from a Swiss bank vault.
Stefan Litt, the library's curator of humanities, said the collection also included drawings. "Parts of them are known, others aren't so - that's maybe one of the most important things," he said.
"...All the writings by Kafka that we have now in our custody will be digitised and will be open for the public worldwide."
Kafka, whose best-known works include "The Trial", "The Metamorphosis" and "The Castle", died of tuberculosis aged 40 in 1924.
His protagonists are often pitted against overwhelming bureaucracies, inhabiting a nightmarish world that was the model for the term "Kafkaesque".
Litt said hoped some of the archive would be available on the Internet by the end of the year.