When did Constantine reunite the roman empire?

Constantine did not reunite the Roman Empire. The Roman empire was never split. Emperor Diocletian had created the tetrarchy (role by four) in 286. This was a system of co-emperorship with four co-emperors. Two of them were senior emperors (Augusti) in charge of the eastern part of the empire (Diocletian) and the western part of the empire (Maximian). The other two were junior emperors subordinated to the senior ones and in charge of the defence of the troubled frontier areas of the river Rhine in the west and the river Danube in the east. These were administrative and defence reform of a a single empire. The terms Western Roman Empire and Eastern Roman Empire have been coined by historians. The Romans had only one term Roman Empire. Diocletian stressed that the Roman Empire was indivisible.

Constantine started as a co-emperor and became sole emperor in 324 after wining two civil wars, one against a usurper (Maxentius) an one against co-emperor Licinius.