Roettgen insisted there was no danger of blackouts.
"We assure that the electricity supply will be ensured at all times and for all users,"he pledged.
The government must now determine how it can make up the difference with renewable energy sources,natural gas and coal-fired plants.
Merkel's spokesman Steffen Seibert said the plan would uphold four priorities:Germany's standing as a top global economy,an affordable and sufficient energy supply,climate protection and independence from energy imports.
The decision is effectively a return to the timetable set by a previous Social Democrat-Green coalition government a decade ago.
It is a humbling U-turn for Merkel,who at the end of 2010 decided to extend the lifetime of the reactors by an average of 12 years,which would have kept them open until the mid-2030s.
That decision was unpopular even before the earthquake and tsunami in March that severely damaged the Fukushima facility,sparking mass anti-nuclear protests in Germany.
Merkel's zigzagging on what has been a highly emotive issue in the country since the 1970s cost her in recent state elections as the anti-nuclear Greens gained ground.
Nuclear opponents slammed the deal and said they would stage fresh demonstrations next month calling for a faster phase-out.
Meanwhile industrial giant Daimler warned the shutdown would undermine the competitiveness of Europe's top economy.
"Turning our backs on an affordable energy supply is clearly a risk,"chief executive Dieter Zetschke told the daily Bild,adding that he saw the decision as"strongly coloured by emotions".
The Fukushima accident has sparked a renewed global debate about the safety of nuclear power,with opinions differing widely.
Sweden's environment minister criticised Germany's decision,saying it would lead to a disjointed energy policy that failed to adequately address climate change.
The United States and Britain have announced plans to build new reactors as an alternative to producing harmful greenhouse gas emissions while ensuring a relatively cheap supply of energy.
Italy scrapped nuclear power in 1987,one year after the Chernobyl disaster,while neighbouring Switzerland said last week it would phase out atomic energy by 2034.