Money is printed by the Department of the Treasury.
The Fed has a unique public/private structure that operates independently within government but not independent of it. The Board of Governors, appointed by the president and confirmed by the Senate, represents the public sector, or governmental side of the Fed. Twice a year, the Chairman of the Board of Governors must report to Congress and one of those times he presents an annual report that includes independently audited financial statements of the entire system. The Board of Governors is a 100% government agency.
The Reserve Banks and the local citizens on their boards of directors represent the private sector. This structure provides accountability while avoiding centralized, governmental control of banking and monetary policy.