What was the written agreement that formally ended Japan's participation in World War II called?

The written agreement that formally ended Japan's participation in World War II was the Japanese Instrument of Surrender.

This document recorded Japan's acceptance of the Allied surrender conditions and was signed on September 2, 1945, aboard USS Missouri in Tokyo Bay. It stated that the Japanese government and Imperial General Headquarters would surrender to the Allied powers and obey the orders of the Supreme Commander for the Allied Powers.

Japanese Foreign Minister Mamoru Shigemitsu signed on behalf of the government, while General Yoshijirō Umezu signed for Imperial General Headquarters. General Douglas MacArthur and representatives of the Allied nations then added their signatures.

The instrument is not the same as the Potsdam Declaration. The declaration of July 26, 1945, demanded Japan's surrender and outlined Allied terms. The instrument was the later document that recorded Japan's formal capitulation. It also differs from the San Francisco Peace Treaty of 1951, which ended the state of war between Japan and many Allied countries.