Biography was not a major literary genre in the ancient world. Of course, historians did include some biographical information in their works, but biography, the story of someone's life, was considered a lesser genre. In the preface to his Great Leaders of Foreign Peoples, the Roman Cornelius Nepos says: 'No doubt, Atticus, most people will judge this type of writing lightweight and unworthy of the characters of great men when they read stories of how Epaminondas taught music or find commemorated among his virtues that he danced well and was a skilful flute player' (my translation). He then goes on to argue that this is due to ignorance of the differences between Greek and Roman cultures.
Cornelius Nepos lived in the 1st century B.C., and although he did not invent the genre, his works are the earliest biographies that have come down to us. He was a friend of Cicero and Atticus, and of Catullus. He wrote full lives of Cicero and Cato the Elder which do not survive, and a series of short lives (most only two or three A4 pages long) in a work called 'Illustrious Men', part of which is the Great Leaders of Foreign Peoples mentioned above. The rest is lost, apart from scattered fragments and lives of Cato the Elder and Atticus from the section 'Latin Historians'.
The Latin text of Nepos' surviving works can be found on the internet at Bibliotheca Augustana, and an English translation at: tertullian.org. There is a Loeb print edition.
Perhaps the greatest biographer of ancient times was Plutarch. He was a Greek, born in the late 40s or early 50s A.D., and he probably lived on into the early part of the reign of the emperor Hadrian (117-138 A.D.). We know that he spent some time in Rome and Alexandria, and that as well as being a citizen of Chaeronea (his home town) he was also a citizen of Athens and a priest of the oracle of Delphi. He wrote a series of 48 lives of famous Greek and Roman political and military figures, divided into pairs, one Greek and one Roman, each pair being followed by a comparison of the two. We only have 46 of these parallel lives (the lives of Epaminondas and Scipio are missing), and not all of the pairs now have a comparison (whether they ever did, we don't know). We also have two lives of Roman emperors (Galba and Otho) from a series of imperial biographies from Augustus to Vitellius, and two miscellaneous lives of Aratus and Artaxerxes. Plutarch was also a prolific essayist on a variety of subjects, and about half of his essays survive.
In a much-quoted passage from the introduction to his lives of Demosthenes and Cicero, Plutarch admits that the small town of Chaeronea is not the best place for a historian to work and that a larger place with access to libraries and scholars might be better.