c. 1300, performen, "carry into effect, fulfill, discharge, carry out what is demanded or required," via Anglo-French performer, performir, altered (by influence of Old French forme "form") from Old French parfornir "to do, carry out, finish, accomplish," from par- "completely" (see per-) + fornir "to provide" (see furnish). Church Latin had a compound performo "to form thoroughly, to form."
Theatrical/musical senses of "act or represent on or as on a stage; sing or render on a musical instrument" are from c. 1600. The verb was used with wider senses in Middle English than now, including "to make, construct; produce, bring about;" also "come true" (of dreams), and to performen muche time was "to live long." Related: Performed; performing; performable.