Germany has approved a package worth up to 500bn euros (£393bn; $683bn), France will spend about 350bn euros, and Spain has set aside 100bn euros.
The bulk of this money will be used to guarantee lending between banks - part of a plan agreed to this weekend by the 15 nations that use the euro.
The cash will also be used to take stakes in ailing banks.
Separately, the major global central banks also said they would offer financial institutions an unlimited amount of short-term dollar loans to help stem the crisis.
UK shares got a boost after the government said it would inject up to £37bn of taxpayer cash into Royal Bank of Scotland (RBS), Lloyds TSB and HBOS.
UK shares got a boost after the government said it would inject up to £37bn of taxpayer cash into Royal Bank of Scotland (RBS), Lloyds TSB and HBOS.
The FTSE 100 index was up 205.5 points, or 5.23%, at 4,137.56 points.
"Today marks another momentous day in both UK and global financial history," said Keith Bowman, equity analyst at Hargreaves Lansdown Stockbrokers.
"Today marks another momentous day in both UK and global financial history," said Keith Bowman, equity analyst at Hargreaves Lansdown Stockbrokers.
"The hope in the markets is that political leaders have finally 'grasped the nettle', with substantial and coherent rescue plans now being formulated and rolled into place.
"The hope in the markets is that political leaders have finally 'grasped the nettle', with substantial and coherent rescue plans now being formulated and rolled into place."
FTSE 100 INDEX: 13 October 2008*All Times GMT
European action
In other key developments on Monday:
The US Federal Reserve, the European Central Bank, the Swiss National Bank and the Bank of England unveiled further measures to thaw frozen credit markets. They said they would provide unlimited dollar funds to financial institutions via money market auctions.
The UK said it would inject up to £37bn of taxpayer money into Royal Bank of Scotland (RBS), Lloyds TSB and HBOS.
Governments in Germany, France and Italy are expected to unveil their bank rescue plans this week, within an agreed eurozone framework.
Reports said that Germany's financial rescue plan would total about 400bn euros ($545bn;£318bn), with Chancellor Angela Merkel due to make a statement later.
Nicolas Sarkozy announces the rescue plan
The Icelandic stock exchange said share trading would remain suspended until Tuesday due to continuing "unusual market conditions".
Trading on the Russian stock market resumed after regulators halted operations last week because of unprecedented volatility. The rouble-denominated MICEX - rose 3.9% to 727.7.
Lifelines
Governments around the world had been racing to throw financial institutions a lifeline before the major markets re-opened.
At the weekend, finance ministers from the main industrialised nations - the G7 - approved a five-point plan to unfreeze credit markets, and a number of countries announced individual rescue packages.
A European plan was confirmed after an emergency Paris summit of the 15 eurozone leaders.HAVE YOUR SAYIt seems Mr Brown and Co. have no choice in this matter and these takeovers are necessary, but its very wrong that it is the tax payer that should have to do thisAnthony Halpin, AberdeenSend us your comments
Under the eurozone plan, members pledged to guarantee loans between banks until the end of 2009, and said they would put money into them by buying preference shares.
"Central banks will continue to work together and are prepared to take whatever measures are necessary to provide sufficient liquidity," the European Central Bank said in its statement.
Australia's Prime Minister Kevin Rudd said his government would guarantee all bank deposits, however large, for the next three years.
The move raised confidence as markets opened, and Australia's central bank on Monday pumped $2bn into the banking system to facilitate improve lending between banks.
Asian shares rally
Australia's benchmark index ended 5.6% higher and South Korea's main Kospi index finished up 3.8%.
Hong Kong shares ended up 9.7% and Shanghai's benchmark index rose 3.65% after falling earlier.
But Taiwan stocks fell 2.15%.
Japan's stock market was closed for a public holiday.
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