The STOXX 600 rose as much as 0.8 percent. The pan-European index later pared gains to close up 0.2 percent as Wall Street fell at the open, giving back part of the rally triggered in the previous session by Powell's comments.
Traders believe the risk of fast-rising interest rates hurting the U.S. economy and the stock market was now on the downside after Powell said monetary policy rate is now "just below" estimates of a level that neither brakes nor boosts a healthy economy.
"If you were looking for a trigger for a December rally in equities, we got it last night from the Federal Reserve," wrote Neil Wilson, chief market analyst for Markets.com.
The improved mood comes after sell-offs in February and October prompted markets analysts to question the sustainability of the longest bull market in recent history.
A Reuters survey published on Thursday showed however that a majority of analysts believe that the upward trend isn't over just yet with more than 40 percent of strategists saying the current run has more than a year to go.
Tech and cyclical stocks, which have been some of the hardest hit in the recent sell-off, were among the leading sectoral gainers on Thursday, while banks were a weak spot.
Deutsche Bank fell 3.4 percent after German prosecutors said police raided six of its offices in and around Frankfurt over money laundering allegations linked to the "Panama Papers".
Deutsche Bank said it was cooperating with authorities.
Elsewhere in the sector, British banks made moderate moves, from HSBC ending flat to Lloyds falling 0.3 percent, after all seven lenders passed this year's Bank of England stress tests.
Shares in Elekta fell sharply at the open after the Swedish radiation therapy gear maker reported an unexpected drop in operating profit, while order intake was slightly short of expectations due to a sharp drop in the Americas.
Elekta stood by its full-year sales and profitability forecast, helping its shares recover and end up 4.5 percent. Morningstar kept its growth expectations unchanged, saying the sharp order drop in the Americas was likely to be short-term.
Britain's Intu < INTUP.L> sank 40 percent after deputy chairman John Whittaker abandoned a plan to buy the British shopping centre group. This reignited worries about the outlook for the battered sector and Intu's rival Hammerson fell 7.5 percent.
(Reporting by Julien Ponthus and Danilo Masoni; Editing by Andrew Heavens)
By Julien Ponthus