Theodoric was nudged to Italy by Zeno to get rid of Odoacer, who was the de facto leader of the Foederati, or ethnic "Barbarians" fighting for Rome (who at this point in time made up most of the army; so much for "The Military of Ancient Rome").

Odoacer had deposed Romulus Augustulus when he lost the army's favor. At this point in time years of civil wars had brought a long succession of army-backed strongmen to power, many of whom had mixed heritage (just like most soldiers); Romulus Augustulus, the last emperor, was himself was a puppet of his father Orestes, who had married into a Roman family but himself was not an ethnic Roman (and to be pedantic, the Eastern Emperor never even recognized Augustulus, which allowed Julius Nepos, the pervious emperor, to rule in semi-autonomy in Dalmatia claiming all the while to be Emperor of the West. This can give you an idea as to how chaotic things had been getting in Italy at this point).

Odoacer, unlike his predecessors, openly admitted that although his "martial law" allowed him to rule Italy, he was powerless beyond the alps, and never called himself Emperor, rather, he sent the imperial paraphernalia to Constantinople and asked to be recognized as "Consul", keeping all of the functions of the Roman administration in Italy intact (indeed, Flavius Odoacer was so Romanized historians aren't even sure which "Barbarian" ethnic group he belonged to). He initially played lip service to the pervious emperor Julius Nepos, who all the while had been hanging out in Dalmatia since Romolus Augustulus deposed him. Odoacer even minted coinage in Julius Nepos' name, but this didn't stop him from from (probably, there's only circumstantial evidence) getting involved in the plot whereby he was eventually murdered. Regardless, after the murder of Julius Nepos, Odoacer asked to be given the title of Patrician by the Eastern Emperor, and be recognized as the ruler of Italy under the wing of a single Roman Emperor in Costantinople.

The Eastern Emperor Zeno, however, didn't have many thoughts to spare Odoacer, he was much too engrossed by his own issues in Costantinople. Zeno had to consolidate his dubious claim to the throne; as an Istaurian (from southern Anatolia) he had few longstanding friends in Constantinople, and he had gained the previous emperor Leo's trust (and his daughter's hand in marriage) thanks to his political maneuvering (read: he tattled on the right people during the right conspiracy). Most importantly, Zeno wasn't much of a military man, having only paricipated in expeditions in Greece equal parts vague and minor save for the usual political conniving and betrayals. So he had hardly had he gained power that his armies were causing him problems, thanks to (among other things) Theodoric.

So Theodoric the Amal, King of the Ostrogoths, raised in Constantinople, was convinced by Zeno to go conquer Italy. The Ostrogoths were largely Romanized, having lived within the Eastern Empire's borders for centuries. They had been given lands in Pannonia in exchange for the defense of the upper Danube, but evidently Zeno came to the conclusion that the Ostrogoths were more trouble than they were worth (having fought against him when they weren't fighting with each other, and in a general sense just being another annoying thing to have to deal with). By sending the Ostrogothic soldiers and their King Theodoric away to Italy, they would stop annoying him, and he could also get rid of Odoacer in Italy, who at this point another potential opponent.

When Theodoric defeated Odoacer and set up the first Kingdom of Italy, he did his utmost to further maintain the Roman institutions, law, and judicial system. However, he did not rule from Rome, rather, he ruled from Ravenna, seaside city conveniently defended by swampy surroundings, and easily supplied by ship.

So here we are, soon after the "Fall" of Rome, the first Kingdom of Italy was established as a client state of Costantinople, and lasted into the sixth century. One political system was substituted for another, and this new system was arguably better suited to the militarized necessities of the time. Relations with Constantinople would weaken and strengthen (mostly weaken) through the years, but there would be no "Shock" that would warrant some sort of easily identifiable unique reaction, as infighting among the Italian ruling class continued much as it did for the past few centuries when the ruler of Italy was calling himself "Imperator" instead of "Rex".

On mobile right now so don't have access to all my sources, but I do know that the "break" from roman rule to ostrogothic rule was far from a completle shift to an entirely new goverment. Theoderick the great was educated in Constantinople and kept most of the Roman legal code intact, as evidenced by his surviving codex, although there were significant differences mainly in that the laws were changed to favor his ostrogothic troops over Romans. But besides that my picture of the time period was that it simply involved the removal of the facade that Romans still held most of the political power instead of their "barbarian" troops. It's important to remember that none of the "barbarian" conquerors wanted to destroy rome. rather, they respected roman civilization and wanted to reinfuse it with ostrogothic martial vigor. It's only until after Justinian the great invaded Italy and threw down the ostrogothic kingdom that truly barbarian barbarians, aka those that did not have direct contact with Romans for centuries like the ostrogothic people had had, such as the Lombard move in. When they finally take over the legal code changes to something that would be trully alien to a traditional roman. An example of this is the concept of trial by combat to prove someone's guilt or lack thereof. I'll try to provide sources when I get home