Crimes recorded by police in England and Wales fell by 7% in the year ending March 2013, according to the Office for National Statistics.
There were reductions in nearly all the main categories of crime including violence, but sexual offences rose 1%.
Separate data from the Crime Survey for England and Wales showed the number of crimes had fallen 9% since a year ago.
And the Home Office said the number of police officers had fallen to below 130,000 - 4,500 fewer than last year.
Prime Minister David Cameron hailed the figures as "good news" at a time of police cuts and thanked the service for its efforts.
"We have asked them to do more with less resources. They have performed, I think, magnificently," he said.
Labour welcomed the figures, but said there was "worrying evidence" the service provided by the police was "being hollowed out" with cuts to the number of officers.
Despite the wider drop in recorded crime, one of the main categories to rise was "theft from the person" - including pick-pocketing and snatching of bags and mobile phones - up 9%.
The stealing of phones out of people's hands as they walk along the street was a particular issue in London, BBC home affairs correspondent Danny Shaw said.
Fraud offences have also seen a big rise, up 27%. Officials suggested this was due to changes in the way fraud was recorded, with a more centralised approach.
The Association of Chief Police Officers (Acpo) said it was also an indication more fraud was being committed online.
Statisticians attributed the rise in sexual offences to the "Yewtree effect" - referring to Scotland Yard's operation set up after the Jimmy Savile scandal.
They suggested the number of sexual offences reported could continue to rise over the coming months, as people come forward to report historic offences.
The Crime Survey, which is based on people's experience of crime and includes offences which aren't reported, now shows offending is at its lowest level since the survey began in 1981.
Our correspondent said levels of crime had been falling since the mid 1990s, but there were some indications the decrease may now be slowing.
On LBC Radio, Deputy Prime Minister Nick Clegg said falling crime figures were "one of the great triumphs of recent years" and "a great tribute to the police".
The Home Office has also released figures on the number of police officers, showing there were 129,584 officers at the end of March - 14,000 fewer than in 2010 and the lowest number of officers since 2002.
Officer numbers fell in 37 of the 43 forces last year - with the largest percentage decreases in the City of London force and Staffordshire. In the Met there were 1,742 fewer officers.
Shadow home secretary Yvette Cooper welcomed the fall in crime, which she said was in line with longer-term trends.
She added: "The police are doing an impressive job in increasingly difficult circumstances... but Acpo have warned that the full effect of the cuts is not yet being felt.
"As the government has made it so much harder for the police, they should not try to take credit for the work the police and communities are doing."