The sovereignty of the Romans over the Byzantine was partially at their own consent. Fed up with being the focus of a long lasting conflict between Bithynia and Macedonia in the 2nd century BC. Byzantium joined with Kyzikos and Rhodos in calling on Rome for aid. It became a subject of the Roman Empire in 146 BC. Formerly self administered, it became a part of the Bithynia-Pontius province, thus maintaining its importance but losing the city-state status it had enjoyed for 700 years Sheltered by the Roman administration, Byzantium experienced a 350 years period of relative peace broken only by the Septimus Severus and Pescennius Niger civil war in the 2nd century AD. The Byzantines had supported Pescennius and following his defeat Septimus wrecked his revenge on the city by massacring many of its inhabitants, burning the city on an even grander scale and Byzantium once again entered a period of relative calm, lasting up until the period of Constantine the Great. In 330 AD., the Roman Emperor, Constantine 1, proclaimed the ancient city of Byzantium as his capital. The newly rebuilt city subsequently became known as Constantinopolis. The imperial city became one on the most prominent political and religious centers in Christendom during the reign of Constantine, who was said to have been baptised as a Christian on his death-bed. Throughout the 4th and 5th centuries, the city became a target of attack, especially by Goth and Vizigoth warriors. Attila the Hun besieged Constantinople in 440 and for ten years extracted taxes from its residents. During this period of chaos, sectarian arguments occasionally escalated into riots and civil wars. In spite of civil unrest, Constantinople managed to retain its international reknown. The city's population exceeded that of Rome, especially after the huge wave of Thracian immigrants in the 5th century. It was during this time that the outlying suburb of Sycae was created (today's Galata); it grew to accommodate the influx of immigrants and became a significant trading site, connected to the metropolis via a bridge. The Western Roman Empire, on the other hand, was in decline. In 476, the Ostrogoths dethroned Romulus Augustine, the Roman Emperor of the West.  Constantinople was soon to become the sole capital of the Roman Empire. (s2)

CONSTANTINE THE GREAT

In AD 324, after defeating his co-emperor Licinius, Constantine the Great became sole ruler of the Roman Empire. One of his greatest achievements was to move the capital of the empire from Rome to Byzantium. Initially, Constantine preferred the site of Troy for his capital, but was persuaded by advisers that Byzantium held a superior position for both defence and trade. Constantine's city was officially styled the "New Rome" but became widely known as Constantinople. The emperor quickly started on an ambitious programme of construction work, which included the Great Palace  and various public buildings.
Constantine was also instrumental in the spread of Christianity. According to legend, he saw a vision of the cross before a battle in 312. Although not actually baptized until just before his death, he worked hard to create a coherent system of Christian belief out of the variant practices of the day. All the early church councils took place in the city or nearby, the first being held in Nicaea, and the second in Constantinople itself.
A successor of Constantine, Theo-dosius I  divided the Empire between his two sons, Honorius and Arcadius. When the Latin-speaking Western Empire fell to barbarian armies during the 5th century, the Greek-speaking Eastern Empire, thereafter known as the Byzantine Empire, survived. (s1)