The pace of expansion slowed slightly to 0.7% in the fourth quarter after the construction sector shrank due to a poor performance in November.
But the figures from the Office for National Statistics (ONS) suggested that the UK has now recovered the lion's share of gross domestic product (GDP) lost during the recession.
ONS chief economic adviser Joe Grice said: "We have now seen four successive quarters of significant growth and the economy does seem to be improving more consistently.
"Today's estimate suggests over four-fifths of the fall in GDP during the recession has been recovered, although it still remains 1.3% below the pre-recession peak."
In 2007, the last year when the pace of growth was faster, the economy grew by 3.4%. In 2012, growth was just 0.3%.
Today's figures show the scale of improvements in the economy's prospects, a year after it was feared that the country was about to sink into an unprecedented "triple-dip" recession.
They provide the latest boost for Chancellor George Osborne after the International Monetary Fund recently upgraded its forecast for growth in Britain - just months after the body told the Government it should rethink its austerity strategy.
But the surprise pace of growth in 2013 saw the economy grow by 0.5% in the first quarter and 0.8% in the second and third three-month periods of the year.
The estimated fourth-quarter figure of 0.7% marks a slowdown as the overall performance was dragged down by the construction sector, which shrank by 0.3%.
This was largely the result of a 4% slump in November - which has previously been disclosed - despite support from Government schemes such as Help to Buy.
Construction remains 11.2% off its pre-recession level in the first quarter of 2008.
Manufacturing improved by 0.9% in the fourth quarter. The sector remains 8.2% off pre-crisis levels.
Services, which represent three quarters of UK economic output, improved by 0.8%. It is now above 2008 levels.
Mr Osborne said: "These numbers are a boost for the economic security of hard-working people.
"Growth is broadly based, with manufacturing growing fastest of all.
"It is more evidence that our long-term economic plan is working.
"But the job is not done, and it is clear that the biggest risk now to the recovery would be abandoning the plan that's delivering jobs and a brighter economic future."
Prime Minister David Cameron tweeted: "The GDP figures are another sign our long-term economic plan is working - more growth means more jobs, security and opportunities for people."
Deputy Prime Minister Nick Clegg said the task of repairing the country's finances must be completed "fairly".
He said: "Our economy is moving in the right direction - unemployment is down and growth is up.
"The coalition Government has set Britain on the right course by repairing the country's finances and helping to create over 1.6 million jobs in the private sector.
"But we must finish the job fairly, with further investment in jobs outside London and by cutting taxes for working people."
For this year, the IMF forecasts growth of 2.4%, in line with the independent Office for Budget Responsibility. The Bank of England's most recent outlook was for growth of 2.8% in 2014.
But James Knightley, of ING Bank, said signs suggested an even better performance.
He said: "Employment continues to rise robustly, housing activity is very firm, confidence is on the rise, credit growth is improving and the UK's key export market - the eurozone - is showing some encouraging signs.
"Consequently, we believe that the economy can post GDP growth of 3% this year."
Howard Archer, of IHS Global Insight, said: "While GDP growth slowed modestly in the fourth quarter of 2013, expansion of 0.7% quarter on quarter still marked a very satisfactory end to a surprisingly good year for the UK economy."
He said the annual rate of expansion placed the UK among the strongest growing major economies last year.
"UK GDP growth of 1.9% in 2013 is essentially double the rate of expansion that has been anticipated at the start of last year."
But Alan Clarke, of Scotiabank, said of the fourth-quarter performance: "While that is a good outcome, it's not great." Separate surveys had indicated it could have been better.
He said a consensus view of 2.5% growth in 2014 was only likely to be improved if exports "start to pull their weight", though this was doubtful given the strong pound and lacklustre demand in the UK's main trading partners.
Another key factor this year could be whether there will be more jobs and higher wages to continue to fuel consumer spending - to "take over the baton" from the reduced saving and higher borrowing that has so far helped it improve.
Martin Beck, UK economist at Capital Economics, said the fourth-quarter figure - coming in below the Bank of England's latest forecast of 0.9% growth - may help to quell calls for an interest rate rise among some members of its Monetary Policy Committee.
He added: "Q4's number provides a good launchpad for a further acceleration in growth this year.
"With rising real incomes set to provide stronger support for household spending and investment set to pick up, we expect GDP to expand by a healthy 3% in 2014."