Rambam in Mishneh Torah Genevah 5:2 says (based on Bava Kamma 114b):
הגונב ומכר ולא נתייאשו הבעלים, ואחר כך הוכר הגנב, ובאו עדים שזה החפץ שמכרו פלוני הוא גנבו בפנינו. חוזר החפץ לבעליו והבעלים נותנין ללוקח דמים ששקל לגנב, מפני תקנת השוק והבעלים, חוזרין ועושים דין עם הגנב.
ואם גנב מפורסם הוא לא עשו בו תקנת השוק ואין הבעלים נותנין ללוקח כלום אלא חוזר הלוקח ועושה דין עם הגנב ומוציא ממנו דמים ששקל לו:
When a thief steals and sells the stolen article before the owner despairs of its return, the thief is discovered, and witnesses come and testify that so and so stole this particular article in their presence, the stolen article shall be returned to its owner. The owner must reimburse the purchaser for the money that he paid the thief. This measure was ordained to enable uninhibited trade in the marketplace. The owner then sues the thief for the money he paid.
If the thief's reputation was known, our Sages did not ordain any leniency. The owner is not required to pay the purchaser anything, and instead, the purchaser must sue the thief and collect the money he paid from him.
This is also confirmed by Choshen Mishpat 356:2. So if the original owner didn't give up the hope and he has witnesses that the guy, who sold you the watch, had stolen it, you have to give back the watch and you can ask the price you paid (I assume that you are not a fence for the second option). The Gemarah discusses in particular, whether it is enough to claim that the item was stolen, and concludes that one may simply spread a word of theft to get back items that were actually sold. This means that the owner has to bring a proof of theft.