In London, the FTSE100 index closed up 119 points, or more than 2 per cent, at 5622.90. The Frankfurt and Paris markets closed up more than 2.5 per cent, while in New York, the Dow Jones was trading up 138.26 points at 8844.41 at lunch-time.
One analyst commented: "There is a much better feeling about the global environment and the worst-case scenario has been substantially reduced."
Far Eastern equity markets also put in a strong showing.
Japan's benchmark Nikkei index hit a seven-week high, closing up 575.06 points, or 4.12 per cent, at 14,527.81.
Analysts attributed part of the Nikkei's strength to the decision by Barton Biggs, Morgan Stanley's chief global strategist, to double the weighting of Japanese stocks in the firm's model international portfolio.
Not all analysts were convinced the crisis was past its peak. Sharda Persaud of Paribas said: "There is a bit of a delayed reaction to Clinton and people are also getting more expectant in terms of European rate cuts. But we're probably seeing a bit of a bear market bounce. I suspect there may still be some bad news out there."
US analysts said the dollar should continue to benefit from the reduced likelihood of presidential impeachment following Democrat victories at the polls.
Yesterday, the dollar was up 1.7 yen at 116.85 yen in morning trade in New York, and 0.6 pfennigs higher against the German mark.
Peter von Maydell, currency strategist at Credit Suisse First Boston said: "The risk that Clinton will be impeached has receded as has the risk of further currency devaluations in Latin America. Equities and the dollar are up as a result."
Major government bond markets slipped as a result of the equity market surge. Analysts said the bonds were losing their "safe haven" appeal. US government bond prices were also hit by recent increases in supply.Reuse content