This name was first used in this spelling by William Shakespeare for a character in his comedy 'Twelfth Night' (1602). Shakespeare may have based it on Oliver or Oliva, or perhaps directly on the Latin word oliva meaning "olive". In the play Olivia is a noblewoman who is wooed by Duke Orsino but instead falls in love with his messenger Cesario.
The name has been used in the English-speaking world since the 18th century, though it did not become overly popular until the last half of the 20th century. Its rise in popularity in America was precipitated by a character on the 1970s television series 'The Waltons'.