1520s, "to give (legal) confirmation to," from Latin corroboratus, past participle of corroborare "to strengthen, invigorate," from assimilated form of com "with, together," here perhaps "thoroughly" (see com-) + roborare "to make strong," from robur, robus "strength," (see robust).
Meaning "to strengthen by evidence, to confirm" is from 1706. Sometimes 16c.-18c. in its literal Latin sense "make strong or add strength to," especially of medicines. Related: Corroborated; corroborating; corroborative.