In the year of 1468, the first Florentine caravel under captain Buonarotti crossed the Atlantic, found the way to the Swedish colony of Nystad. They discovered the Potomac river, and since the area was yet unclaimed by Sweden, they claimed it for Florence. They named the land Italia Nuova (New Italy) and founded Roma Nuova at the site of OTL Richmond.
1543, with Scandinavia in Civil War / unrest, the other powers used the opportunity. Nystad, the capital of New Sweden, was taken by the Dutch; the South and West of the Chesapeake peninsula went to Italia Nuova. The Netherlands and Florence made a treaty, ruling the border between their colonies in Atlantis, and promising to respect their borders.
In the same year, Florentine troops stood in Naples and the Marches. Now however, the main army of the Rum-Seljuks arrived, and the Florentine army was defeated several times. The chaos allowed many carbonari to leave South Italy and flee to safer places. Many would settle in Italia Nuova, which soon included all of Virginia and Maryland (although thinly settled).
During the 1570s, the influx of Southern Italians in Florence had lead to the rich merchants being questioned about their lifestyle. In reaction, the Matthewan movement started, which defends their wealth. (Like OTL Calvin's teachings, they drew biblical support for their theory from the "Parable of the talents", from the Gospel of Matthew.) The duke ruled that the Matthewan interpretation of the Bible was the right one, and dissenters were displaced to the mountain areas of Italia Nuova.
In 1589, French who explored the source of the Tennessee river, found the way to Italia Nuova. The Appalachians became the border between Italia Nuova and French Louisiane.
During the 1670s, Italian settlers who were trying to cross the Appalachians were defeated by Atlanteans allied with the French.
1688, when Florence united with Sicily to form the kingdom of Italy, Italia Nuova was also drawn into the anti-French War. In 1692, Friedrich von Hohenzollern, a German in the service of the governor of Italia Nuova, performed "The wild ride", fought his way through the French colony of Caroline with his cavalry troops, finally linking up with the Spaniards in Florida. In the peace of Amsterdam 1694, Louisiane north of the Arkansas was divided between Italy (gaining the whole South) and Denmark-Braunschweig (the North).
Since ~1700, poor Italians (mostly from the South), often with differing religious ideas, settled west of the Appalachians, in the Tenesi (yes, OTL Tennessee) area.
Around 1800, settlement had reached the Rocky Mountains, where the Italians decided to stop.