c. 1200, tumbe, early 14c. tomb, from Anglo-French tumbe and directly from Old French tombe "tomb, monument, tombstone" (12c.), from Late Latin tumba (also source of Italian tomba, Spanish tumba), from Greek tymbos "mound, burial mound," generally "grave, tomb."
Watkins suggests it is perhaps from PIE root *teue- "to swell," but Beekes writes that it is probably a Pre-Greek (non-IE) word. He writes that Latin tumulus "earth-hill" and Armenian t'umb "landfill, earthen wall" "may contain the same Pre-Greek/Mediterranean word," and suggests further connections to Middle Irish tomm "small hill," Middle Welsh tom "dung, mound."
The final -b began to be silent about the time of the spelling shift (compare lamb, dumb). Modern French tombeau is from Vulgar Latin diminutive *tumbellus. The Tombs, slang for "New York City prison" is recorded from 1840.