Westerwelle made the announcement after meeting NTC officials, including its foreign minister Ali al-Essawi.
"We want a free Libya, in peace and democracy without [Moamer] Kadhafi," he said in Benghazi, Libya's second city.
Germany becomes the 13th nation to recognise the NTC as "sole legitimate representative".
France was the first to do so, followed by Australia, Britain, Gambia, Italy, Jordan, Malta, Qatar, Senegal, Spain, the United Arab Emirates and the United States.
Fighting between Kadhafi's forces and rebels raged across Libya, with casualties reported in the western town of Zintan and the strategic oil port of Brega in the east.
Battles were also being fought in the Berber mountains south-west of Tripoli, in nearby Yafran, and at Dafnia near Misrata, Libya's third city, according to the rebels.