How long has Professor Binns been a professor at Hogwarts?

Question

How long has Professor Binns worked at Hogwarts for, dead or alive?

I'd also be interested in a date of death.

Answer 1

Worked at Hogwarts for something like 50 to 250 years; died before 1942, but after the mid 1800s.

_{Note: This answer is a bit of a stretch, and involves a lot of guesswork, but it's probably the best you'll get.}

Ghosts, like portraits, tend to not register any events after their death.

No physical pleasure remains to them, and their knowledge and outlook remains at the level it had attained during life, so that old resentments (for instance, at having an incompletely severed neck) continue to rankle after several centuries.
_{(Pottermore - Ghosts)}

Based off of this we can set some bounds for his death.

Professor Binns seems to have no memory of the first time that the Chamber of Secrets was opened, so we can assume that he died sometime before 1942.

“That will do,” he said sharply. “It is a myth! It does not exist! There is not a shred of evidence that Slytherin ever built so much as a secret broom cupboard! I regret telling you such a foolish story! We will return, if you please, to history, to solid, believable, verifiable fact!”
_{(Harry Potter and the Chamber of Secrets - Chapter 9)}

Professor Binns uses Bathilda Bagshot's A History of Magic as a class textbook, so he must have been alive while it was published. We do not know exactly when Bathilda Bagshot was born^†, but we know that she was already an adult when Kendra Dumbledore arrived in Godric's Hallow around 1890 (dating based on Percival Dumbledore being imprisoned "scarcely a year" before Albus went to Hogwarts.)

Thus, we can probably assume that Professor Binns died sometime roughly around 1860-1940.

As for how long he taught at Hogwarts before he died, the most we have to go on is that he was "ancient", "shriveled", and "very old" when he died.

Ancient and shriveled, many people said he hadn’t noticed he was dead. He had simply got up to teach one day and left his body behind him in an armchair in front of the staff room fire; his routine had not varied in the slightest since.
_{(Harry Potter and the Chamber of Secrets - Chapter 9)}

Professor Binns had been very old indeed when he had fallen asleep in front of the staff room fire and got up next morning to teach, leaving his body behind him.
_{(Harry Potter and the Philosopher's Stone - Chapter 8)}

The closest thing we have to a canonical image of him is this Pottermore illustration:

We do know that Wizards often live up to 150 years (Faris Spavin was 147 when he retired), and that some Professors were hired at the age of 21, so we can probably put an upper bound as having taught for ~130 prior to death.

_{†Fantastic Beasts and Where to Find Them does give us a publication date for A History of Magic, but I am choosing to pretend that was the publishing date of a later edition. "Anyone interested in a full account of this particularly bloody period of wizarding history should consult A History of Magic by Bathilda Bagshot (Little Red Books, 1947)."}

Answer 2

There appears to be ZERO canon information on the topic (aside from the DUH Obvious that he died before Harry Potter started attending his lectures).

I have checked:

• Interviews on accio-quote

• Pottermore article "Hogwarts Ghosts"

• Pottermore article "The 6 best-loved ghosts (and one poltergeist) at Hogwarts"

• Books

• Wikia article on Binns

• HP Lexicon

Curiously, Pottermore Wikia's article on Binns says he was born in 16/17th century and died in 18th century - but does NOT reference that at all, this info is NOT on Pottermore. I suspect someone made it up because of Goblin Rebellion lectures?

There's a barely-canon (in HP:PS video game) suggestion that he taught James Potter (src: http://harrypotter.wikia.com/wiki/Vault_998), but we don't know if he was alive or a ghost during the time.