Ancient Mediterranean basin, being the economical and cultural center of Europe, tended to be on the receiving end of migrations patterns since the Bronze Age up to Celts. Romania, by virtue of having unified and expanded these mediterranean cores from one hand and having projetted deeply in Barbaricum its influence (Roman military material was recently found in Poland, for instance) only increased this tendency : Cimbric-Teutonic migration is a prime example of this.
While mentioning, as
@Byzantion does, the Hunnic migration, isn't wrong it's essentially the immediate cause only : settlement of Barbarians within Romania appeared before in the form of laeti and some early Rhenish foedi. The long-term causes were rather what I mentioned above, and the climatic changes of the IIIrd century that (added with the civil wars of the Empire and Sassanian pressure) greatly reduced Barbarian capacities of local subsistuance (most of the grain in Germania was imported) and turned to groups of population being on the move well before Huns appeared in Vth century Europe.
Long story short, you can't butterfly away migrations of Barbarians and formation of Barbarian peoples as Goths on the limes because it's a by-product of the Roman Empire.