The show, first broadcast in 1957, will be shown on BBC4 in a monthly half-hour slot from February with repeats on BBC2.
No decisions have been made about the presenter's role, which has been filled by a series of guest stars following the death of host Sir Patrick Moore last December, aged 89.
Kim Shillinglaw, head of commissioning science and natural history, said: "Sir Patrick Moore inspired generations of astronomers and I hope that alongside the BBC's other astronomy content, such as BBC2's Stargazing Live, The Sky At Night will enthuse further generations about the wonder of the night sky."
More than 40,000 fans signed a petition in support of the show following reports it could be axed.
Until his illness, Sir Patrick missed only one episode in the show's history.