The wider FTSE-100 index rose 69.49 points, or 1.2%, to 5640.64, its highest close for nearly two months, with banking shares among the biggest risers.
Barclays' shares rose 5.6p to 168.4p after Mr Agius announced his departure, with analysts advising shareholders to snap up the stock following heavy falls last week.
David Jones, chief market strategist at IG Index, said Mr Agius's resignation was "a step in the right direction".
The improved sentiment was driven by last week's agreement in Brussels, which will allow struggling banks to take financial aid directly from the European Union without the debt adding to governments' debt mountains and driving up their borrowing costs.
Lloyds Banking Group was ahead 0.4p at 31.5p, Royal Bank of Scotland rose 3.7p to 219p and HSBC advanced 9p to 570.1p.
The improved sentiment came despite figures revealing that eurozone unemployment hit another record in May as the financial crisis pushed the continent toward the brink of recession.
The Dax in Germany and the CAC 40 in France were both up more than 1%.
However, the Dow Jones industrial average in New York was down 0.5% as the London market closed, after data showed the manufacturing sector shrank in June for the first time in nearly two years, fuelling fears of a slowdown in the world's biggest economy.
The pound was up against the euro at 1.25 as the single currency lost some of the gains it made in the wake of the European summit last week.
However, sterling was down against the dollar at 1.57 as the greenback was hit by the worrying manufacturing data.
In corporate news, AstraZeneca was 29p higher at £28.82 after it announced a partnership with Bristol-Myers to buy US group diabetes specialist Amylin for $7 billion (£4.4bn).
Oil firm Soco International was 7% higher after it agreed to buy the remaining 20% it does not already own in its Vietnamese subsidiary from Lizeroux Oil & Gas for $95m (£60m). The shares rose 20p to 309.4p.
Among the biggest Footsie risers were Aviva, up 10.1p at 282.7p, and Petrofac, 49p firmer at 1437p.