Initial reports say the category three storm caused no serious damage.
It passed as forecast to the south of the Isle of Pines which was the only part of the territory on full alert.
The system brought gales of up to 130 km an hour as well as heavy rain.
Hilary Roots, who lives on the Isle of Pines, said Cyclone Gita was frightening as it passed through Friday night.
She said there was less rain than forecast but there were very strong wind gusts.
Ms Roots said the eye passed a hundred kilometres to south of the Isle.