London's benchmark FTSE 100 index rallied 1.55 percent to 6,054.04 points compared with Thursday's close.
In the eurozone, Frankfurt's DAX 30 jumped 1.77 percent to 9,594.53 points and the Paris CAC 40 won 1.75 percent to 4,423.12.
European stock markets had closed lower Thursday following another volatile day of trading, as a spreading Volkswagen scandal offset positive German data.
But equities fought back Friday, mirroing gains in Tokyo, after Yellen hinted at a US rate hike by the end of 2015.
"With equities having sold off following the Fed’s decision to leave rates on hold last week, the bullish (market)... reaction suggests investors would prefer the Fed to get on with it and raise rates sooner rather than later," said Mike van Dulken, analyst at Accendo Markets trading group.
Yellen on Thursday said that she still expects to increase interest rates in 2015 and that concerns about weaker global growth was unlikely to affect the plan.
Her remarks came a week after the US central bank opted at a widely anticipated meeting against enacting the first rate hike in nearly 10 years.
Following the September 17 meeting, Yellen told a news conference that the committee decided to hold off owing to worries about slowing growth in China and capital flight from emerging markets.
But in Thursday's speech, Yellen said policymakers were still "monitoring developments abroad" but did not think they would derail the US economy.
"As we come to the end of a turbulent (trading) week, where pretty much every sector has felt the chill winds of selling pressure, the health of the global economy continues to come under singular scrutiny, with emerging markets in particular the source of increasing concern," said Michael Hewson, chief market analyst at CMC Markets UK.
"We continue to hear a lot of reassuring words that China’s economy is not heading for a hard landing, and while that may be true major corporates appear to be concerned enough to take steps to shore up their balance sheets."
Highlighting the volatility of the past week, shares in auto giant Volkswagen shot up by more than four percent at the open on Friday, ahead of the widely anticipated announcement of its new chief executive.
VW shares, which have bounced back over the past two days from unprecedented losses at the start of the week, hit an intraday high of 117 euros in the first few minutes of trading, an increase of 4.3 percent from the closing price the day before.