Victories from Anne Keothavong and Elena Baltacha secured the win to ensure a perfect start to Judy Murray's reign as team captain.
Britain had to win group matches against Portugal, the Netherlands and Israel to set up the play-off clash with the Austrians and they then proceeded to win the promotion play-off in style.
First up, Keothavong came from an early break down to defeat Austria's Patricia Mayr-Achleitner 7-6 (5) 6-3.
Then Elena Baltacha won the first 16 points against Tamira Paszek on her way to a dominant 6-1 6-4 victory to seal promotion.
"We did it! So, so happy right now! Great Britain Fed Cup team are just rocking it," said Keothavong on Twitter.
Britain have competed in every Fed Cup tournament since it began in 1963 but have never won it.
They have reached the final four times but not since 1981. Their World Group II play-off will take place in April.
