The pound has hit a two-year high against the euro and a two-week high against the US dollar, after Scotland voted against independence.
The FTSE 100 share index was up 0.6% at 6,861 in early trading, BBC reported.
On the currency markets, sterling rose 0.4% to 1.2743 euros and jumped nearly 0.8% to $1.6525 against the US dollar, before falling back slightly.
Meanwhile RBS confirmed it would not be moving its registered head office now that independence had been rejected.
"The announcement we made about moving our registered head office to England was part of a contingency plan to ensure certainty and stability for our customers, staff and shareholders should there be a 'Yes' vote," the bank said.
"That contingency plan is no longer required. Following the result it is business as usual for all our customers across the UK and RBS."
In a statement, Lloyds Banking Group said: "The group is proud of its strong Scottish heritage and remains committed to having a significant presence in Scotland. We remain fully focused on supporting households and businesses in Scotland as well as right across the rest of the UK."
Relief
Over the past couple of weeks the pound had fallen on fears that Scotland would vote in favor of independence.
Jeremy Cook, economist at World First said: "The obvious risk to the currency markets was a yes and that would have caused a big sell off. Now the markets will go back to concentrating on the fundamentals of the UK economy."
Shares prices in London opened higher, with RBS up more than 3% and Lloyds Banking Group up nearly 2%.
Brenda Kelly from IG Index said: "Investors in these firms will be relieved that management will be able to devote their time to business performance, rather than fretting about contract changes or headquarter moves.
"There is still uncertainty, primarily over the new changes to voting on English issues, but these are of importance primarily to politicians and less so to markets," she added.
Asset managers with strong exposure to Scotland led gains on the FTSE. Wealth manager St James's Place led gains, up more than 4%, while Schroders was up more than 2%.
The main Spanish share index, the IBEX, was the strongest performer in Europe, up 1.3%. That was attributed to the 'No' vote because it was seen as reducing the chances of a breakaway in Catalonia.
The boss of Aberdeen Asset Management, Martin Gilbert, who had previously said that Scotland "would prosper" as an independent country, also welcomed the end to the uncertainty of the last few months.
"Scotland has long been a world leader in business sectors such as oil and gas, and investment and the task now is to grow the rest of the economy with the strong support of politicians of all parties," said Gilbert.
Disruption Avoided
Analysts also said that the result reduced the risk of the UK leaving the European Union.
"Scottish residents are more in favor of remaining in the EU, compared to the rest of the UK where the majority favor an exit. Overall, major disruption has been avoided and focus can now return to building on the strong economic recovery in progress, " said Azad Zangana, economist at Schroders.
"The Bank of England is now likely to press ahead with raising interest rates early next year in the absence of political uncertainty," he added.
Stock markets in Asia were mostly higher, taking their cues from Wall Street.
US stocks rose on Thursday, one day after the central bank – the US Federal Reserve – said it would maintain its pledge to keep interest rates low. Those comments helped to lift the Dow Jones Industrial Average and the S&P 500 index to record highs.
The FTSE 250, which contains the next biggest companies after the FTSE 100, was up more than 1%.
The main Spanish share index, the IBEX, jumped more than 1% in early trade, but fell back in the afternoon to trade 0.4% higher. That was attributed to the 'No' vote because it was seen as reducing the chances of a breakaway in Catalonia.
Sterling wasn't the only thing with a spring in its step this morning. Business leaders who had expressed concerns about the possibility of independence will also be relieved that all those contingency plans for possible upheaval can be put away – for the foreseeable future at least.
Business attention will now quickly turn to the constitutional changes announced by the prime minister Thursday morning. Although initially it may not seem a business matter, greater federalism in the UK could have significant ramifications.
There may never be an English Parliament – I'm sure the last thing voters want is more politicians – but if powers over the setting of taxes and business policies for example are devolved to the four nations of the UK, then chief executives will have to sit up and take notice.
