The Munich-based Ifo think tank's closely-watched business climate index, based on a monthly survey of some 7,000 firms, rose for a third straight month to 110.6.
That was more than a full point higher than the December reading of 109.5, above a Reuters consensus forecast for 110.0 and the highest reading since July 2011.
Ifo economist Klaus Wohlrabe said the strong survey suggested the German economy could grow by 0.5 percent in the first three months of the year, roughly double the rate expected for the fourth quarter.
"January's Ifo survey suggests that the German economy has started the new year with a reasonable amount of momentum," said Jonathan Loynes, Chief European Economist at Capital Economics.
In its monthly report, the Bundesbank said it expected economic growth to pick up between January and March as the industrial sector gains traction. It pointed to strong improvements in both the export and production outlook.
Surveys last week showed the German private sector growing at its fastest pace in more than 2-1/2 years and investor morale staying close to its highest level in nearly eight years, boding well for the first quarter.
But economists warned that the economy's performance last year was not as strong as "soft" privately-produced survey evidence would have suggested.
"The small growth conundrum of the German economy continues. While soft indicators remain buoyant and both consumer and business confidence are close to all-time highs, hard data has been lagging behind and still is," ING economist Carsten Brzeski said.
Still, the latest hard data has shown increases in industrial output, orders, exports and retail sales.
FIRMS OOZE OPTIMISM
While Germany was a growth locomotive in the early years of the euro zone crisis, its performance has tailed off over the last two years and it only managed an expansion of 0.4 percent in 2013, its weakest performance since the global financial crisis.
But economists predict gross domestic product (GDP) will increase by around 1.7 percent this year thanks to strong domestic demand while exports are also expected to pick up. Berlin is considering raising its forecast to 1.8 percent from 1.7 percent, a German magazine reported at the weekend.
The Bundesbank said GDP likely increased "very strongly" at the end of the year thanks to growing domestic demand, stronger appetite for German goods from abroad and support from the industrial sector.
The Ifo survey showed firms were more optimistic about their future prospects than they have been in nearly three years and were more upbeat about their current business situation than at any time since June 2012.
German car parts and tyre maker Continental AG said earlier this month it expected sales to keep growing this year and Beiersdorf, the maker of Nivea skin care creams, reported its highest level of underlying sales growth in five years in 2013.
Manufacturers and construction companies, which had a subdued start to 2013, began this year in better form, with factories becoming more positive about their export prospects, Ifo said.
Retailers were slightly more downbeat overall than in December but they still expected business to pick up in the next six months, boosting hopes that private consumption will help drive stronger GDP growth this year.