The FTSE 100 Index added 147.52 points, or more than 2.48 per cent, to 6,109.01, after a 70-point fall in the previous session.
It meant London’s top-flight finished a volatile week just above last Friday’s closing level of 6,104.1.
A decision by the Fed not to lift rates earlier this month had added to anxiety because it appeared to imply the US economy was not ready to withstand a hike yet given risks from the rest of the world.
But Yellen’s remarks that global weakness will not be significant enough to stop a rates rise this year removed some of the uncertainty facing markets.
Tony Cross, market analyst at Trustnet Direct said although Yellen’s speech appears to have been sufficient to reassure investors and drive equity markets higher he added: “Just how sustainable this will be remains to be seen and with the official Chinese PMI numbers for September due for release before the end of next week, there’s certainly scope for the skittish conditions to return.”
On currency markets, sterling was down slightly against the US dollar at just under 1.52 and little changed against the euro at slightly above 1.35.
In London shares, banks - which stand to gain from a higher interest rate environment - were among those making gains.
Barclays rose more than 3 per cent, or 8.5p, to 255p, while HSBC added 15.5p to 503.6p and Royal Bank of Scotland climbed 8.3p to 319p.
Fellow state-backed lender Lloyds Banking Group added 1.7p to 75.5p as it was announced that the Government had sold another 1 per cent chunk of the group to take its stake below 12 per cent.
Platinum metals company Johnson Matthey, the world’s largest supplier of vehicle catalytic converters, continued its strong recovery after being hit by the escalating Volkswagen scandal. Shares climbed almost 5 per cent, or 116p at 2,514p.