The U.S. Treasury controls the printing of money in the United States. However, the Federal Reserve Bank has control of the money supply through its power to create credit with interest rates and reserve requirements. Since credit is the largest component of the money supply by far, colloquially people talk about the Federal Reserve increasing the money supply as printing money.
However, this thought process is technically not true as the Federal Reserve has no control over the printing of currency. (The Treasury controls and operates the printing presses.) Instead, the Fed functions as a bank for all the other banks in the country. It lends money to banks and maintains financial stability by tweaking reserve ratios and interest rates to balance the twin objectives of maximum employment and price stability.
The Printing Money Myth
The myth that the central bank prints money became prevalent following the Great Recession, when many were concerned about the unconventional policies of the central bank, which included intervention in the commercial paper market, mortgages and outright purchases of debt to keep the system from collapsing. Both during and in the aftermath of the recession, the Federal Reserve expanded its balance sheet, peaking at roughly $4.5 trillion from late 2014 through 2016.
Many who were against an interventionist central bank opposed this credit creation as printing money, which would lead to hyperinflation. The Federal Reserve and its defenders argued its policies were more of a reaction to economic conditions and the absence of expansionary fiscal policy. With the crisis in the rear view, there has been no inflation and the U.S. economy has outperformed its counterparts, vindicating the actions of the Federal Reserve as not being merely money printers.
The Treasury Department's Role
The Treasury Department is actually the entity responsible for printing paper currency and minting coins, overseeing the Bureau of Engraving and Printing (BEP), and the U.S. Mint. As of January 2018, there was approximately $1.61 trillion in cash in circulation. When banks need cash, they request it from the Federal Reserve. The Federal Reserve electronically deposits it into the bank's account and charges the appropriate interest rate. When they have excess cash on hand, banks return it to the Federal Reserve, settling any accounts.
The Federal Reserve has 12 regional banks that supervise banks in local areas. These regional federal banks are responsible for meeting the physical currency needs of local banks, providing cash and taking excess cash. They also take currency out of circulation when it is deemed to be damaged, counterfeit or just too old. They order newly printed bills and coins from the BEP to replace discarded notes and coins. For 2018, the Federal Reserve Board of Governors ordered almost 7.4 billion new notes to be printed, which total $233.4 billion. About 75% of these notes replace those removed from circulation.
(For related reading, see: Understanding How the Federal Reserve Creates Money.)