At Greenspan's final meeting on Tuesday, the central bank voted to boost its target for the federal funds rate to 4.5%.
It was the 14th quarter-point move in a credit-tightening campaign that began 19 months ago.
The increase will raise borrowing costs for millions of American consumers and businesses as banks were expected to quickly boost their prime lending rates by a similar quarter-point. The prime rate stood at 7.25% before Tuesday'smeeting.
Many private economists believe that the Fed is likely to raise rates at least one more time at its next meeting on 28 March although the Fed modified its statement on Tuesday to give Greenspan's sucessor, Ben Bernanke, more leeway.
Bernanke, a former Fed board member who since last summer has been George Bush's chief economic adviser, is scheduled to take over on Wednesday as the Fed's 14th chairman since the central bank was created in 1913.
The central bank modified Tuesday's statement to remove the word "measured", which it had been using to signal further gradual quarter-point moves.
New chairman Ben Bernanke was
Bush's chief economic adviser
Instead, the central bank said that "some further policy firming may be needed" to keep inflation under control.
That was a slight change from the December meeting when it had said that measured policy firming is likely to be needed.
The goal of the central bank has been to push interest rates up as a way of slowing the economy and making sure that low inflation - probably Greenspan's biggest legacy - will remain under control.
To commemorate Greenspan's final day, photographers and television camera crews were allowed in for the first time to photograph a portion of the meeting of the Federal Open Market Committee, the panel of Fed board members and regional Fed bank presidents who meet eight times a year
behind closed doors to set interest rates.
Greenspan and his colleagues ignored the photographers' pleas to turn towards the cameras although the requests did elicit chuckles from the group.
The 79-year-old plans to open his own economic consulting business to be called Greenspan Associates. He has already selected office space in Washington.
The Fed has been aiming for a neutral federal funds rate - a level where the economic growth is not being stimulated or held back - and many analysts believe that is somewhere below 5%.
Many economists believe the Fed will stop raising rates with one more increase to 4.75% on 28 March.