The simple answer is that he did not. This is a later Byzantine conceit. What Constantine was probably doing was building a tetrarchic capital like Thessalonika, Sirmium, or Nikomedeia before him. If we define a Roman capital as a having something special that only Rome had (in this case, the praefectus urbi) then Constantinople only became a capital in 359. The praetorian prefect also seems to have only been based out of Constantinople from the 370s, so this was an ongoing project. Only under Valens and Theodosius do we see the major construction projects that the city needed, such as the aqueduct, which was critical since a limiting factor in Byzantion's size previously had been a lack of accessible water. Constantine's choice in naming the city after himself might have been to establish himself as a name-giving Romulus. In general, the most reasonable treatment of this topic that I've seen is: Errington, R. Malcolm. Roman Imperial Policy from Julian to Theodosius. Chapel Hill: University of North Carolina Press, 2006.