Gabriel de Broglie, chancellor of the prominent academic society, proclaimed himself surprised and delighted by the news.
"C'est une grande joie!" ("It is a great joy"), de Broglie said by telephone.
The full contents of the four-page letter - by the philosopher best known for the phrase Cogito, ergo sum ("I think, therefore I am") - are to be published this year.
Bos, a research fellow at Utrecht University in the Netherlands, said the letter offered an invaluable view of Descartes' mind at work - describing how he decided to exclude certain material from his famous work of 1641, Meditationes de prima philosophia.
The find had a special resonance for Haverford president Stephen Emerson, who read Descartes as a philosophy major when he attended the school in the 1970s.
"I remember reading the 'Meditations' as if it were yesterday," he said. "It's the beginning of modern Western philosophy."
The letter is one of 12,000 in a rich trove of autographed documents collected by Haverford alumnus Charles Roberts, who graduated in 1864. They include letters and other paperwork signed by a wide range of literary figures, politicians and other notables, from Abraham Lincoln to Queen Isabella of Spain.
Roberts is believed to have purchased the letter from a dealer, and school officials said there was no indication he knew it was stolen.
The path to that discovery began last month in the Netherlands, when Bos conducted one of his periodic Google searches for Descartes documents. Haverford had recently published a list of the Roberts letters online, and the Descartes missive popped up on Bos' screen.
He immediately fired off an e-mail to John Anderies, head of special collections at the college. Anderies simply scanned the letter and e-mailed it to Bos.