Westerwelle also held talks with Yemen new President Abdrabuh Mansur Hadi during a brief visit to Sanaa on Saturday before heading to neighbouring Saudi Arabia that evening.
Westerwelle paid tribute to the "peaceful transition" in which Hadi last month replaced veteran strongman Ali Abdullah Saleh. The former president ceded power in line with a Gulf-brokered deal following months of mass pro-democracy protests demanding his removal, Saba said.
The new president will be serving for a two-year transitional period. Germany said it was ready to help Yemen rebuild.
"Developments in Yemen have shown that the political solution is possible. Peaceful transition is necessary and it must be understood by other countries," Saba quoted Westerwelle as saying Saturday.
This was apparently a reference to Syria, where at least 8,500 people have been killed in a regime crackdown on dissent, according to the Syrian Observatory for Human Rights monitoring group.
The German foreign minister also announced that his country will provide €265 million to help rebuild Yemen.
Germany will attend a "Friends of Yemen" forum of aid donors in Riyadh in April, the foreign minister said, according to Saba.
On Saturday evening Westerwelle travelled to Saudi Arabia where he is due to hold talks with officials on the violence in Syria, diplomats said.