By every account that I found so far, the Republican Anicii appear to have originated in Praeneste, a town due east of Rome. Although Praeneste did not gain the franchise until much later, the Anicii of Praeneste were obviously Roman citizens, and quite possibly members of the Ordo Equester, but as this is sheer speculation, it would be impossible to say whether they were senior knights, holding the Public Horse, or more junior in social rank.
Thus far, the first member of this family that I have found reference to is one M. Anicius Gallus who served as a Tribune of the Plebs in 247 BC. Two years later, another Tribune of the Plebs, Quintus Anicius Praenestinus appears. I have very little regarding either of these gentlemen, however, because of the details I have discovered regarding Lucius Anicius Gallus (see below), who shared the name of the first Tribune, and the same point of origin as the second, I am reasonably sure that both these Tribunes were members of the same family.
Aside from these notices, which provide no further information, the next reference is made by Livy which mentions a statue in Praeneste in honor of one Marcus Anicius, who served as the commander of the garrison at Casilinum in 216 BC, presumably defending against Hannibal.
The next notable mention regards Lucius Anicius Gallus, a praetor, who served as a legate under Paulus Aemilius in the Third Macedonian War. In his role as legate, he successfully conquered Illyria and captured its king, who was featured in his triumph in Rome. Later, he became Consul of Rome in 160 BC. This gentleman was noted as being from Praeneste and as being the who ennobled his family.
The Anicii again appear to vanish from the histories until AD 65, when one Gaius Anicius Cerealis appears in the Senate of the early Empire. Though known as a sycophant and traitor to the Republican cause, this senator held a number of honours and was consul designate in AD 65. He did not, however, serve as consul, or if he did it was only briefly, as he was killed by Nero the next year. It is around this time that Livy (xlv.43) mentioned the Anicii and ranks them below the great families of Rome.
The Anicii again vanish until the mention of Sextus Cocceius Anicius Faustus Paulinus who served as proconsul in Africa, circa 260. This gentleman is beyond any doubt the forefather of the later Imperial Anicii, however, as of yet, I have been unable to determine whether or not he was desceded from, or related to, any of the previous Anicii. From a genealogical point of view, this gentleman represents the beginning of the family which became such a power in the later Roman world.
From these beginnings, the Anicii continued to expand, establishing branches of the family throughout the Empire and accumulating fantastic wealth and prestige. Although they were of the highest nobility from this time on, they were rather unconventional in some respects. They were, along with the Bassi, Gracchi, and Paulini, among the first senatorial families to adopt Christianity in 402 or 404. Gibbon suggests that this conversion was a political move meant to atone for the Anicii support of Maxentius by adopting the faith of Constantine I, though if this was true, it must have been a sincere conversion, as from this time, the Anicii were unpopular with the pagans of Rome. Again, after Italy fell to Odovacar, the Anicii behaved most unconventionally by joining with the Decii in supporting Odovacar against the Eastern Empire.
Among the notable Anicii of the later Empire was the Emperor Anicius Olybrius, the great Eastern matron Anicia Juliana, the philospher Anicius Manlius Severinus Boethius, and the bishop Ennodius.