The number of people unemployed in the UK fell by 34,000 to 2.47m in the three months to May, official figures show.
Meanwhile, those claiming Jobseeker's Allowance fell in June by 20,800 to 1.46m, the Office for National Statistics (ONS) said.
That took the jobless rate to 7.8%, the lowest since January and below forecasts of about 7.9%.
The number of people in work rose by 160,000 in the three months to May, the biggest rise since August 2006.
However, the increase was due to a record 148,000 rise in the number of part-time workers, while full-time workers increased by just 12,000.
The ONS said the percentage of workers in part-time jobs was 27%, its highest since records began in 1992.
The figures will raise hopes that the economic recovery is gaining momentum. Although some experts think unemployment could start rising again by the end of next year. 'Stable' market
Andrew Sentance, a member of the Bank of England's Monetary Policy Committee, said in a speech on Tuesday that the labour market had stabilised.
"Evidence from the Bank of England's agents and recent employment surveys is that the labour market in the UK has stabilised and that labour demand in the private sector may have already started to pick up."
David Tinsley, an economist at National Australia Bank in London and a former Bank of England official, agreed that rising unemployment had come to an end - for now.
"It may pick up again next year. It's hard to see how a steady pace of improvement will be maintained as public-sector job losses start to bite."
Vicky Redwood, of Capital Economics, was also cautious about future downward trends. "We still doubt that private sector hiring will pick up strongly enough to offset the severe public sector job cuts," she said.
The UK jobless rate compares with 10% in the eurozone, 9.5% in the US and 5.2% in Japan, the ONS report showed.Pay rises slow
Meanwhile, the ONS reported that wage growth eased sharply in the three months to May, with average weekly earnings growth falling to 2.7% from 4.1% in the three months to April.
Stephanie Flanders, the BBC's economics editor, said: "The bottom line is that UK households are still seeing a significant squeeze in living standards as a result of the financial crisis, even if more people than expected have found paying work.
"And, lest we forget, the squeeze from higher taxes and lower public spending has barely begun," she said.