By mid-afternoon, London's benchmark FTSE 100 index was more or less flat compared with the close on Wednesday.
But in the eurozone, Frankfurt's DAX 30 added 0.1 percent and the CAC 40 in Paris won 0.4 percent.
Europe's main indices had already jumped by between 1.2 and 1.6 percent on Wednesday after Yellen pledged a "gradual" approach to US interest rate increases.
The Fed news boosted investor appetite for risky assets like equities, dealers said.
"Risk appetite is back in force after Janet Yellen hinted that the cost of borrowing could increase slower than previously thought," said London Capital Group analyst Ipek Ozkardeskaya.
Forex.com analyst Fawad Razaqzada agreed.
"Yellen came across as more dovish than expected. Stock markets love low interest rate levels and for that reason they were able to rise sharply which lifted the Dow to a new all-time high," he said.
Playing catch-up following another overnight record-high on Wall Street, Asian indices mostly surged Thursday.
In closely watched testimony to Congress, Yellen said the US central bank would keep lifting borrowing costs as long as the world's top economy showed improvement, taking into account inflation remained below its two percent target.
The remarks lit a fire under equities, with the Dow posting its highest close, on the prospect that money would continue to be cheap for the time being.
The Fed is watching developments carefully, Yellen told the House Financial Services Committee during the first of two days of testimony on Capitol Hill.
Later on Thursday, she will appear before the Senate Banking Committee.
In Asia, Hong Kong stocks jumped 1.2 percent to its highest level since mid-2015 and Sydney climbed 1.1 percent.
Shanghai was 0.6 percent stronger after data showed Chinese imports and exports both rose more than expected in June thanks to a pick-up in global demand.
Tokyo ended flat however with early gains eroded by a stronger yen, which hit exporters.
While equity markets were mostly sharply higher, the dollar came under pressure as expectations for further monetary tightening from Washington this year eased.
There had been talk of late that the Fed would announce up to two more increases in rates before the end of the year.
Adding to downward pressure on the greenback is the ongoing crisis surrounding Donald Trump after his son released emails showing he had embraced Russia's efforts to support the tycoon's presidential campaign against Hillary Clinton.
The White House has been battered by accusations over Russian collusion and accusations of cover-ups -- fuelling worries about the president's ability to push through his market-friendly economic agenda.