"I rejoice with the people in Egypt," she said.
"We are witnessing a historic change. I call on those who now bear the responsibility and will bear the responsibility to make the developments in Egypt irreversible, and that they keep the peace," she told reporters.
She said the military leadership now running the country must also do its part to uphold peace in the region.
"We also expect the future Egyptian government to continue to keep the peace in the Middle East, in that the agreements made with Israel are respected and Israel's security is guaranteed," she said.
Merkel said she wished the Egyptian people "a society without corruption, censorship, arrests and torture," adding that Mubarak had done his people "a final service" with his resignation.
"The legitimate demands made by the people in recent days must be implemented quickly. We will do everything in our power to support the developments in Egypt, the legitimate wishes of the people," she said.
"We believe it is essential that this transformation is truly irreversible and that it results in a freer Egypt. At the end of the process there must be free elections."
Meanwhile in New York, German Foreign Minister Guido Westerwelle welcomed Mubarak's resignation as "a historic moment."
"The chance for democratic change must be used now," Westerwelle said at the United Nations where he is holding talks.
He said Germany was willing to help the new leadership "with this transformation process in a close partnership."