The exporter-heavy FTSE 100, which makes around 70 percent of its income abroad and tends to benefit from a weaker pound, rose 1.1 percent, while the more domestically focused FTSE 250 index added 1.2 percent.

"Theresa May's Brussels success comes laden with some potentially deal-sinking domestic caveats, namely the House of Commons' 'meaningful vote' expected to be held on 12th December," said Forex.com analyst Connor Campbell.

Financials gave the biggest boost to the FTSE with shares in banks HSBC, Lloyds and Barclays rising between 1.6 and 2.4 percent after EU leaders finally sealed a Brexit deal, saying the package agreed with Prime Minister Theresa May was the best Britain will get.

Their gains also reflected strength in the broader European banking sector which rallied to reports that Italy could lower its budget deficit target to avoid a disciplinary procedure from Brussels.

Oil stocks were also in demand as crude prices clawed back some losses from a nearly 8-percent plunge the previous session.

Shares in Royal Dutch Shell and BP both rose 1.5 percent, while energy services firm John Wood Group gained more than 4 percent to lead gainers on the FTSE after HSBC upgraded the firm to buy.

Faroe Petroleum surged 24 percent after Norway's DNO launched a hostile bid to buy the independent oil and gas company for around 608 million pounds.

Faroe Petroleum rose to 156.5 pence per share, topping the 152 pence offered by DNO.

Among the few losers on the FTSE was Melrose, down 5 percent after Sky News reported that the industrial company had got lower-than-expected bids for its Powder Metallurgy unit.