FPÖ chief Heinz-Christian Strache said that the reversal was agreed in ongoing talks to form a coalition with the conservative People's Party (ÖVP) following elections in October.
"I am proud of this excellent solution in the interests of non-smokers, smokers and restaurant owners," Strache, who had made the move a key campaign pledge, said on social media.
"The freedom to choose lives on. The existence of restaurants (particularly small ones) has been secured. Thousands of threatened jobs have been saved," said Strache, 48, himself a smoker.
Unlike in most of Europe, in Austria people can smoke in eateries under certain conditions -- which are widely flouted -- including that it is confined to separate rooms.
The outgoing government, a coalition of the ÖVP and the Social Democrats, passed a law in 2015 banning smoking completely in bars and eateries, which was due to take effect next May.
The new government, which Strache and non-smoker ÖVP head Sebastian Kurz, 31, want installed before Christmas, will however make some concessions, media reports said.
Under-18s will not be allowed in smoking rooms of bars and restaurants, smoking will be outlawed in cars if under-18s are inside, and the minimum age for smoking will rise from 16 to 18.