Joshua Wong and Nathan Law were imprisoned in August after Hong Kong's government pushed for harsher sentences -- rather than the initial community service orders they were given.
The government's appeal was seen as further evidence of Beijing's growing influence over the semi-autonomous city and its desire to crush a burgeoning independence movement.
Wong, 21, who became the face of Hong Kong's pro-democracy movement while still a teenager, was imprisoned for six months. Law, 24, was sentenced to eight months. They were bailed last month pending an appeal.
Fellow protester Alex Chow, who was jailed for seven months but had not previously applied for bail, was also at the hearing Tuesday.
Chief Justice Geoffrey Ma said the right to appeal was granted because the questions involved were of "great and general importance".
All three were bailed and ordered to appear in court on January 16.
"We are optimistic," Joshua Wong said ahead of the hearing outside Hong Kong's court of final appeal. Dozens of supporters had gathered, holding up yellow umbrellas, the symbol of the mass rallies in 2014.
The Umbrella Movement called for fully free leadership elections to replace a system where the city's chief executive is selected by a pro-Beijing committee.
But months of protest that brought sections of the city to a standstill failed to win concessions.
Since then there have been growing signs that China is increasing its control over the city, with Beijing particularly incensed by activists' calls for Hong Kong's independence.
Hong Kong has been governed under a "one country, two systems" deal since 1997, when Britain handed the territory back to China. The deal allows citizens rights unseen on the mainland, including freedom of speech and a partially directly elected parliament.
Wong vowed on Tuesday that Demosisto, the political party he co-founded last year, would continue to fight for democracy.
A number of leading campaigners have been charged in relation to the 2014 protests, while six pro-democracy legislators -- including two pro-independence activists -- were disqualified from parliament.
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