During the 5th and 6th centuries AD, Byzantium (the Eastern Roman Empire) boasted a host of astrologers: Hephaestion, Julian of Laodicea, "Proclus," Rhetorius, and John Lydus. Though their works are singularly unoriginal compilations, they remain the major sources for an understanding of earlier Hellenistic astrology. By the end of the 6th century, however, the general decline of the Byzantine Empire's intellectual life and the strong opposition of the church had combined to virtually obliterate astrology, though some practice of reading celestial omens survived in Byzantium as it did in western Europe. The science was revived only in the late 8th century and the 9th century under the impact of translations from Syriac and Arabic. The period from about 800 to 1200 was the most propitious for Byzantine astrology, though nothing was essentially added to astrological theories or techniques.
For instance, Manuel I Comnenus, emperor of the Byzantine Empire between 1143-1180, utilized astrology in his political and personal life, as well as supporting translations of occult literature in his court. When the Church Patriarch presented Manuel with a letter from a simple monk claiming that the astrological teaching was a sacrilege, Manuel could not allow a charge of heresy to be leveled against him. He composed a defense of astrology, asserting that it was compatible with Christian doctrine. Only as he became ill and eventually died in 1180, on the advice of Theodosius (Patriarch of Constantinople), he renounced to astrology.
Source: The Alexiad - by Anna Comnena
Byzantine Princess Anna Comnena (1083-1148) was the daughter of Emperor Alexius Comnenus of the Byzantine Empire (or Eastern Roman Empire). When the first Crusaders reached Constantinople (=ancient Byzantium, todays Istanbul), Anna witnessed their arrival and their alien customs, and would later record her observations for posterity in a 15-volume work: the Alexiad. She is considered the world's first female historian.
The "Alexiad" of Anna Comnena has long been used as a source of information by historians of the Byzantine Empire. Here's an excerpt from the Book VI of the "Alexiad" where Anna Comnena expresses her views on astrology and astrologers of her time, starting from a fulfilled forecast by the philosopher Symeon Seth on the death of Robert Guiscard:
"A certain mathematician named Seth who boasted much of his knowledge of astrology had forecast Robert's fate by an oracle, after his crossing to Illyria, written this forecast on a paper, sealed it and entrusted it to some of the Duke's intimates, bidding them keep it till a certain time. After Robert's death they opened it by the astrologer's order and the prophecy was as follows: "A great enemy from the west shall fall suddenly after having stirred up great confusion."This caused everybody to marvel at the man's knowledge; and in truth he had delved very deeply into this branch of science, and if I may be allowed to make a short break in the course of my history, the following are the facts about astrological prophecies. The discovery is fairly recent, and the science of it was not known to the ancients. For  this method of divination did not exist in the time of Eudoxus, the greatest of all astronomers, neither did Plato have any knowledge of it, and even the astrologer, Manetho, had not brought it to perfection. Now these (astrologers) observe the hour of the birth of the persons about whom they intend to prophesy, and fix the cardinal points and carefully note the disposition of all the stars, in short they do everything that the inventor of this science bequeathed to posterity and which those who trouble about such trifles understand. We, also, at one time dabbled a little in this science, not in order to cast horoscopes (God forbid!), but by gaining a more accurate idea of this vain study to be able to pass judgment upon its devotees. I do not mention this for the sake of boasting, but to prove that during my father's reign many of the sciences made great progress, as he honoured both philosophers and philosophy itself, but towards this teaching of astrology he showed some hostility, I believe because it tended to make people of a guileless nature reject their faith in God and gape at the stars. This was the cause of the Emperor's waging war against the teaching of astrology. Yet in spite of this there was no dearth of astrologers at that time, for the Seth I have mentioned flourished then, and there was also a famous Egyptian, Alexandreus, who was a strong exponent of the mysteries of astrology. He was consulted by many and used to give most accurate forecasts in many cases, not even using the astrolabe, but made his prophecies by a certain casting of dice. There was nothing magical about that either, it was an art practised by the Alexandrians (or by Alexandreus). When the Emperor saw how the young people flocked to him and regarded the man as a species of prophet, he himself consulted him twice and each time Alexandreus gave very correct answers. But the Emperor was afraid that harm might come to many from it and that all would be led away to the vain pursuit of astrology, so he banished him from the capital, assigned Raedestus as his dwelling-place and showed great consideration for him, and his means of living were amply supplied from the imperial treasury. Nay more, the great dialectician, Eleutherius, also an Egyptian by birth, cultivated this art too and carried it to such perfection that he yielded the palm to no one. Later again, a man called Catanances from Athens came to the capital, anxious to carry off the first prize among astrologers and when questioned by some about the date of the Emperor's death, he foretold it as he thought, but was proved wrong in his  prognostication. It happened, however, that the lion which was kept in the palace died that day, after four days' fever, so the vulgar considered that the prophecy of Catanances had been accomplished. After some considerable time he again foretold the date of the Emperor's death and was mistaken; yet the Emperor's mother, the Empress Anna, died on the very day Catanances had foretold. Because Catanances had made repeated mistakes in his predictions about him, the Emperor did not like to banish him as he was self-convicted, and also it might seem that he banished him in anger. But now let us return to the point in our history where we abandoned it, otherwise we shall be thought to be stargazers, obscuring the main theme of our history with the names of astrologers."
Another important testimony on the situation of Byzantine astrology we get from the historian Niketas Choniates in his work "O City of Byzantium. The Annals of Niketas Choniates."
As Niketas Choniates depicted him, Alexius III was very keen on astrology and its interpretations of the daily circumstances. Although Choniates considers this a common practice of the emperors of the times, he does not fail to thoroughly criticize it and ridicule those who professed it. He accuses them of denying Divine Providence and perversely turning to interpreting the movements, positions and configurations of the stars, misusing expressions like 'it is fated' or 'what is ordained by necessity...cannot be undone' in order to explain the paradoxes of life.
Niketas' objection to astrology is very well depicted in his account of Manuel I. He blames Manuel for believing in the astrologers as if they were uttering the word of God.
In the episode of Manuel's illness and death, Choniates seizes the opportunity to expose and deride astrologers, as well as criticizing the emperor's belief in their assertions.
"But those pestilential astrologers had the audacity to say that the emperor would shortly recover from his illness...they shamelessly predicted the razing of enemy cities to the ground. What was more outrageous, they, being quick-tongued and used to lying, foretold a great commotion of the universe... the transformation of the whole natural order, thus proving themselves ventriloquists rather than stargazers. They... told the weeks in which these things would happen, and notified the emperor accordingly;... as if they had clear knowledge of the things which the Father has kept in His own power, and about which Our Savior reprimanded his disciples for asking. So not only did the emperor seek out caves... and prepare them for habitation..."
Likewise, Niketas denounces Alexius' inclination on astrology which he finds totally incompatible with Christian faith.