Wikipedia:
The authority of the Federal Reserve Banks to issue notes comes from the Federal Reserve Act of 1913. Legally, they are liabilities of the Federal Reserve Banks and obligations of the United States government. Although not issued by the Treasury Department, Federal Reserve Notes carry the (engraved) signature of the Treasurer of the United States and the United States Secretary of the Treasury.
At the time of the Federal Reserve's creation, the law provided for notes to be redeemed to the Treasury in gold or "lawful money." The latter category was not explicitly defined, but included United States Notes, National Bank Notes, and certain other notes held by banks to meet reserve requirements, such as clearing certificates.[8] The Emergency Banking Act of 1933 removed the gold obligation and authorized the Treasury to satisfy these redemption demands with current notes of equal face value (effectively making change). Under the Bretton Woods system, although citizens could not legally possess gold (except as rare coins, jewelry, for industrial purposes and the like), the federal government continued to maintain a stable international gold price. This system ended with the Nixon Shock of 1971, and starting in 1975 Americans were allowed to possess unlimited amounts of gold with its value dependent on the market price. Present-day Federal Reserve Notes are not backed by convertibility to any specific commodity, but only by the collateral assets that Federal Reserve Banks post in order to obtain them.