The UK's inflation rate, as measured by the consumer prices index, fell to 1.9% in January.
The rate fell below the Bank of England's 2% target for the first time in more than four years.
The fall is likely to underline the Bank of England's message that there is no rush to raise interest rates.
Inflation as measured by the Retail Prices Index rose to 2.8% from 2.7% in December, the Office for National Statistics (ONS) said.
The lower inflation was in large part due to a fall in the cost of recreational and cultural activities, including falling DVD prices and lower entrance fees to attractions.
Discounts on furniture and household goods, and also lower alcohol and tobacco prices, also had an impact, the ONS said.
Prime minister David Cameron tweeted that the figures support the government's economic strategy.
"Today's fall in inflation is more evidence our long term economic plan is working," Mr Cameron tweeted. "We want to ensure a secure future for hard-working people."
Labour said that the fall in inflation would be unlikely to have much of an impact on working people.
"This small fall in the inflation rate is welcome, but with prices still rising much faster than wages the cost-of-living crisis continues," shadow Treasury minister Cathy Jamieson said.
Bank of England governor Mark Carney indicated earlier this month that interest rates would not rise for some time.
The fall in inflation is likely to help bolster this message, according to the British Chambers of Commerce (BCC).
"An economic environment of low inflation and low interest rates allows people and firms to plan ahead, as they can be confident they will not encounter any unwelcome surprises," said BCC chief economist David Kern.
Inflation should fall further over the coming months, according to Samuel Tombs, an analyst at Capital Economics.
"The fall in import prices in response to the stronger pound should feed through to the shops later this year," Mr Tombs said.
The pound fell against a basket of currencies on Tuesday on the expectation that interest rates would not rise.
Traders had pushed sterling to a five-year high on Monday, speculating that rates would soon climb.
The pound fell from $1.6686 to $1.6655, before regaining some ground and rising to $1.6670.
The euro rose against the pound from 82.21 pence to 82.38 pence.