The Dow Jones rose 140.55 to a new closing record of 11,722.98, easily topping Thursday's record. The new closing high was the third this week and the fourth since the start of 2000.
Broader market measures also finished with solid gains. The NASDAQ composite index rose 107.28 to 4,064.49.
The stock rally comes a day after Greenspan's speech before some of the market's top movers and shakers, which reinforced many analysts' opinions that the board will raise interest rates next month.
During his speech, Greenspan gave investors what they expected, every indication that interest rates will be headed higher in February. The Fed chairman also gave an upbeat assessment of the economy, noting that next month it will become the longest expansion in U.S. history.
"There can be little argument that the American economy, as it stands at the beginning of a new century, has never exhibited so remarkable a prosperity," Greenspan said.
The speech convinced many investors the Fed is likely to raise rates no more than a quarter-percentage point at the next Federal Open Market Committee meeting on Feb. 1-2.
Although rate increases are usually troublesome, market watchers said they were impressed that Greenspan indicated he wouldn't let inflation get in the way of a surging U.S. economy.
"Greenspan has demonstrated that he understands the world has changed and that he doesn't intend to do anything scary to the market," said Charles Pradilla, chief investment strategist at SG Cowen Securities. "We are comfortable with Greenspan's comments because it shows he is not behind the curve, and won't let inflation raise its mighty head."
Greenspan said that when economists look back at the current period a decade from now, they may well conclude "at the turn of the millennium, the American economy was experiencing a once-in-a-century acceleration of innovation which propelled forward productivity, output, corporate profits and stock prices at a pace not seen in generations, if ever."
He strongly hinted that higher rates are the only way to restore balance in the booming economy and prevent it from overheating.
"In the end, balance is achieved through higher borrowing rates," Greenspan said.
Some of the Fed chairman's key concerns include unemployment's 30-year low, the steadily falling pool of workers and the soaring stock market with record high after record high.
On top of all that, consumer demand by the end of the 1999 retail sales season saw its biggest gain in 15 years.
Greenspan said that added consumer demand is taxing the economy's resources and if not moderated could lead to rising inflation because of tight labor markets and stretched production capacity.
"It is this imalance between growth of supply and growth of demand that contains the potential seeds of rising inflationary and financial pressures that could undermine the current expansion," Greenspan said.
Calling Greenspan's comments a "thoughtful speech," Treasury Secretary Lawrence Summers said the administration continues to believe the best approach to managing the economy is ensuring that the government's policies support good economic fundamentals.
The Fed has raised interest rates three times in the past six months in an effort to slow the economy and relieve pressures on tight labor markets before they trigger inflationary wage demands.