Support from strong exports is expected to boost internal demand as well, with a pick-up in household consumption providing yet another pillar of growth in what should be a "more broad-based" upswing, a Bundesbank statement said.
The forecast illustrates a growing split between robust activity in core eurozone countries and weak growth or recession in members on the periphery of the 16-nation bloc such as Greece, Ireland and Spain.
For 2010, the Bundesbank estimated that economic activity would expand by its fastest pace since German reunification in 1990.
The German economic recovery "will continue in the next two years following the impressive catching-up process in the current year," a statement said.
"Exports will remain the main driving force behind the upturn" and strong trade will also boost domestic demand, the bank forecast.
Investments in capital goods and construction will benefit from low interest rates as well, while household consumption will be underpinned by a healthier labour market and higher wages, it added.
In 2012, the number of unemployed workers is expected to drop below three million, while the unemployment rate should fall from 7.5 percent at present to 6.9 percent, the forecast said.
Inflation was tipped to come in at 1.7 percent next year and edge down to 1.6 percent in 2012.
The growth estimates are slightly more conservative than those presented by the European Commission for Germany, which foresee growth of 3.7 percent this year followed by 2.2 percent and 2.0 percent in the following two years.
In peripheral eurozone countries meanwhile, austerity budgets aimed at curbing excessive public deficits and reducing debt are expected to weigh heavily on the economy.
"There is a big unknown about all the consolidation measures, how they will affect the domestic economy, especially private consumption, in many countries," UniCredit economist Alexander Koch told new agency AFP.
The European Union's Eurostat statistics service has forecast a contraction of 4.2 percent in Greece this year, followed by a further drop of 3.0 percent in 2011.
In Ireland, which has just received a massive bail-out from the EU and International Monetary Fund, Eurostat sees a contraction of 0.2 percent followed by growth of 0.9 percent. And in Spain, a much larger eurozone economy, the EU forecast is for a drop of 0.2 percent this year and growth of 0.7 percent in 2011.
The Bundesbank warned moreover that downside risks to its own forecast "originate from the persistent uncertainties in the financial markets due to the fragile position of public finances in a number of industrial countries."
But Koch noted that "in Germany for the time being, with dependable exports you clearly have a functioning business model."
"The growth outlook and the situation concerning private household debt is therefore much better here in Germany, it's a much better growth environment."