The principal source for the story is an English translation of Plutarch's "Life of Mark Antony", from the Lives of the Noble Grecians and Romans Compared Together. This translation, by Sir Thomas North, was first published in 1579. Many phrases in Shakespeare's play are taken directly from North, including Enobarbus' famous description of Cleopatra and her barge:
I will tell you. The barge she sat in, like a burnish'd throne, Burn'd on the water: the poop was beaten gold; Purple the sails, and so perfumed that The winds were love-sick with them; the oars were silver, Which to the tune of flutes kept stroke, and made The water which they beat to follow faster, As amorous of their strokes. For her own person, It beggar'd all description: she did lie In her pavilion—cloth-of-gold of tissue— O'er-picturing that Venus where we see The fancy outwork nature: on each side her Stood pretty dimpled boys, like smiling Cupids, With divers-colour'd fans, whose wind did seem To glow the delicate cheeks which they did cool, And what they undid did.
This may be compared with North's text:
"Therefore when she was sent unto by diverse letters, both from Antonius himselfe, and also from his friends, she made so light of it and mocked Antonius so much, that she disdained so set forward otherwise, but to take her barge in the river of Cydnus, the poope whereof was of gold, the sailes of purple, and the oares of silver, which kept stroke in rowing after the sound of musicke of flutes, howboyes cithernes, vials and such other instruments as they played upon the barge. And now for the person of her selfe: she was layed under a pavilion of cloth of gold of tissue, apparelled and attired like the goddesse Venus, commonly drawn in picture: and hard by her, on either hand of her, pretie fair boys apparelled as painters do set foorth god Cupid, with little fans in their hands, with which they fanned wind upon her."—The Life of Marcus Antonius
However, Shakespeare also adds scenes, including many portraying Cleopatra's domestic life, and the role of Enobarbus is greatly developed. Historical facts are also changed: in Plutarch, Antony's final defeat was many weeks after the Battle of Actium, and Octavia lived with Antony for several years and bore him two children: Antonia Major, paternal grandmother of the Emperor Nero and maternal grandmother of the Empress Valeria Messalina, and Antonia Minor, the sister-in-law of the Emperor Tiberius, mother of the Emperor Claudius, and paternal grandmother of the Emperor Caligula and Empress Agrippina the Younger.