The surplus - the strongest since 2009 - compares with £2.8 billion a year earlier and a loss of £516 million in 2011 after the second most expensive year on record for the industry.
The market, which is made up of 91 underwriting syndicates, incurred net claims of £9.6 billion last year, down from £10.1 billion the previous year.
It said UK flooding claims from 2013 are not expected to result in significant exposure for Lloyd's.
New chief executive Inga Beale, who took the helm in January, said: "Disciplined underwriting and a benign year for major catastrophes have enabled us to outperform our peers and post this outstanding profit of £3.2 billion.
"From this base, the Lloyd's market has a great opportunity to expand in the underinsured, high growth economies around the world."
Today's result came after Lloyd's generated record premium income of £26.1 billion last year, with a return on capital of 16.2%. Continued low interest rates reduced investment income to £839 million from £1.3 billion.
The most expensive event to rock the market was Hurricane Katrina in 2005, which caused claims worth 4.3 billion US dollars (£2.8 billion).
Lloyd's recently unveiled Vision 2025, which sets out plans to grow the business in faster growing markets and to make London the "global hub" for specialist insurance and reinsurance by 2025.
Among previous changes to modernise the market, Lloyd's has introduced a new franchise structure and phased out the number of Names who backed the market with an unlimited liability.