"This is a good day for those who bet on a political and diplomatic solution," Westerwelle said, calling Rowhani's speech to the UN General Assembly "encouraging."
He was later set to meet Iran's new leader, who has made diplomatic overtures in his country's nuclear standoff with the West.
Westerwelle emphasized the "stark contrast" between the wording of Rowhani's speech and the fiery broadsides of his predecessor Mahmoud Ahmadinejad against Israel and the United States that prompted Western
diplomats to walk out.
"The Iranians could be serious with a new constructive approach," he said but cautioned that Tehran must take concrete steps to prove its willingness to engage.
"It is critical that new substantial offers are made," Westerwelle added.
Germany's top diplomat also praised US President Barack Obama's speech to the General Assembly, who pushed for a "diplomatic path" with the new Iranian government.
Obama has sent a "strong signal" and offered a "window of opportunity" to end hostilities between Iran and the West, he said.
Westerwelle will participate in high-level talks on Iran's suspect nuclear programme on Thursday, joining counterparts from the United States, Britain, China, France, Russia and Iran.
On Syria, Westerwelle urged world leaders to make renewed efforts for a political process during their annual gathering in New York.
"There cannot be a military solution in Syria. Only a political solution can bring sustainable peace and stability," he said.
Westerwelle is scheduled to address the UN General Assembly on Saturday in what will likely be his last major appearance as foreign minister.
After four years at the helm of Germany's diplomatic corps, Westerwelle is set to leave office following his party's crushing defeat in Sunday's parliamentary elections.