The exact number is unknown, but she has to be over 1000 years old. This is because she locked her sister away in the moon, and she got out 1000 years afterword. It is also stated that, before Luna became Nightmare Moon, they lived in peace for hundreds of years. So I believe she is over 2000 years old.
Well, to answer this question, we must put together facts. We have to think of fillyhood. And at this point, we could say she might have spent a few hundred years as a filly. So there's that. And then they say that they spent hundreds of more years together in peace. So Celestia was most likely already a couple of thousand years old before Luna was sent to the moon. So that's about 4,000 yrs old. And then when Celestia and Luna destroyed Sombra and Discord, they looked adult. So that adds on a few more thousand years. So now that's about 7,000. We come to the area when Luna is sent to the moon. So I'd say that now 9,000 yrs. And then Luna returns, so 10,000. And then we have the 2 yrs that we have so far, but that doesn't matter. So therefor, Celestia is about 10,000 yrs old. Yup, there's what I think! Hopefully my answer seems logical :3