London's FTSE index closed up 1.92 per cent at 3926.38 points.
Russia's battered stock exchanges recovered some of last week's losses when trading resumed on Tuesday after a one-day suspension.
Tracking rising global markets, and following reports that the government had
started buying shares, the benchmark RTS index advanced 4.8 per cent to close at 575.6 points.
Mosocw's MICEX gained 4.1 per cent to end the day at 534.9 points.
Ben Bernanke, the chairman of the US Federal Reserve, and his colleagues began a two-day meeting on Tuesday to make a fresh assessment of economic and financial conditions and decide their next move on rates.
Their decision will be announced on Wednesday.
John Terrett, Al Jazeera's correspondent at the New York stock exchange, said: "The markets have already priced in a 50 points base cut.
"There is talk the European central bank may move with them [the US federal reserve] tomorrow in a co-ordinated move."
Earlier on Tuesday, Japan saw early losses reversed as the benchmark Nikkei index ended the trading day up by 6.4 per cent, giving some much-needed optimism after hitting a 26-year low on Monday.
A weakening of the yen against the dollar encouraged investors to buy shares in exporters such as Toyota and Sony, whose overseas earnings are threatened by a strong yen.
Shares in Toyota ended the day up 7.8 per cent, while Sony's share price finished up by 9.6 per cent and Honda rose by 14 per cent.
Nonetheless, the Nikkei remains far from a full recovery, having lost nearly 40 per cent of its value in the past month amid continuing widespread gloom over the global economic outlook.
Analysts say there is little long-term confidence in share markets, with expectations of more upheaval in the days and weeks ahead.
In Hong Kong on Tuesday the benchmark Hang Seng index saw a rebound, jumping 14.4 per cent after losing more than 12 per cent on Monday.
Tuesday's close was the biggest percentage gain in 11 years.
Bargain-hunters snapped up stocks in companies like banking company HSBC, which had slumped on Monday to levels last seen during the outbreak of the deadly Sars virus in 2003.
HSBC stock rallied by 20 per cent – its biggest one-day gain in 20 years.
South Korea's Kospi index also recovered after early losses, ending the day up 5.6 per cent.
Domestic investors were given a boost following the biggest rate cut ever by the central bank on Monday, snapping up shares in Samsung Electronics, which rose 5.8 per cent, and Hyundai Motors, which jumped 12.6 per cent.