early Middle English tame "in a state of subjection, physically subdued, restrained in behavior" (c. 1200); of animals "domesticated, reclaimed from wildness," also, of persons, "meek, gentle-natured, compliant, intent on homely or domestic activities" (mid-13c.), from oblique forms of Old English tom, tam "domesticated, docile."
This is reconstructed to be from Proto-Germanic *tamaz (source also of Old Norse tamr, Old Saxon, Old Frisian, Middle Low German, Middle Dutch tam, Old High German zam, German zahm "tame," Gothic tamjan "to tame").
This in turn is said to be from PIE *deme- "to constrain, to force, to break (horses)" (source also of Sanskrit damayati "tames;" Persian dam "a tame animal;" Greek daman "to tame, subdue," dmetos "tame;" Latin domare "to tame, subdue;" Old Irish damnaim "I tie up, fasten, I tame, subdue"). A possible ulterior connection is with PIE *dem- "house, household" (see domestic (adj.)).
Gentle animals are the naturally docile; tame animals are made so by the art of man. The dog, the sheep, are gentle animals ; the wolf, the bear, are sometimes tame. [William Taylor Jr., "English Synonyms Discriminated," London: 1813]
The meaning "spiritless, weak, dull, uninspiring, insipid" is recorded from c. 1600. Related: Tamely; tameness.