early 14c., conveien, "to go along with;" late 14c., "to carry, transport;" from Anglo-French conveier, Old French convoiier "to accompany, escort" (Modern French convoyer), from Vulgar Latin *conviare "to accompany on the way," from assimilated form of Latin com "with, together" (see con-) + via "way, road" (from PIE root *wegh- "to go, move, transport in a vehicle").
Meaning "communicate by transmission" is from late 14c. Sense of "act of transferring property from one person to another" is from 1520s. It was a euphemism for "steal" 15c.-17c., which helped broaden its meaning. Related: Conveyed; conveying.