President Truman did not sign a peace treaty with Japan. World War II hostilities ended formally on September 2, 1945, when Japanese representatives signed the Instrument of Surrender aboard the USS Missouri in Tokyo Bay.
General Douglas MacArthur, as Supreme Commander for the Allied Powers, accepted the surrender on behalf of the Allies. The document was signed by Japanese Foreign Minister Mamoru Shigemitsu and General Yoshijiro Umezu.
A formal peace treaty, the Treaty of San Francisco, was signed by 48 nations on September 8, 1951, and came into force April 28, 1952, officially restoring Japan's sovereignty.