"I often say that the euro is more than a currency and we should not forget that in these weeks and months we spend working to strengthen the euro. The euro is more than a currency because at the end of the day it is about the original idea of a union of peace and of values," Merkel told reporters.
Kohl called the honour a "wise and far-sighted decision."
Kohl, a driving force behind European enlargement and integration in the years after the Berlin Wall fell and frequently mentioned as a possible Nobel laureate for his efforts, said he was "very pleased" with the choice.
"The 2012 Nobel Peace Prize is above all an affirmation of the European peace project," the 82-year-old said in a statement.
"It is also encouraging for all of us to continue on the path of a united Europe, which means to work toward ever-greater cooperation on our continent and to develop Europe despite difficulties and problems that still must be surmounted."
Kohl, who was also one of the founders of the euro single currency, said that Europeans had grounds to be "proud."
"I am, and I wish God's rich blessings for our continued path toward a united Europe," he said.
"We see it as affirming, encouraging the great peace project that the European Union spread across the European continent, which rarely knew long periods of peace," said government spokesman Steffen Seibert.
Seibert said the prize was a "joy for all who live in the 27 member states".
"The German government and the chancellor (Angela Merkel) congratulate the EU, its institutions and all their staff on this year's Nobel prize," he said.
In a separate statement, German Foreign Minister Guido Westerwelle called the announcement "a great decision that makes me proud and happy."
"European integration is the most successful peace project in history," he said.
"From the rubble of two horrible world wars, peace and freedom have grown and mortal enemies have become good friends and inseparable partners."
He said the Nobel prize would "spur" Europe "to now get down to solving our own problems, to make an example of our European model of cooperation and to bolster our European efforts for the world's peaceful development."