The cat became domestic four centuries ago, but the cats left Africa 6000 before that. On Cyprus people found domestic cats in graves that were 9500 years old. While Cyprus originally didn’t have any cats. This probably means that cats were taken to there when the rodents and humans arrived.
The cats may be brought to the island on purpose to kill the rodents, but it would take thousands of years before the domestic cat was taken along on ships for company, mascots or merchandise. Cats were valuable and wanted and salesmen could easily trade them.
Phoenician salesmen took the cat 3000 years ago to Great-Brittain. The romans were introduced to the cat 1000 years later when they conquered Great-Brittian. Over the centuries the cats managed to travel north, and around 100 DC to may have arrived to the south of Russia, the north of Europe and to the far east where they accompanied the Christians, Muslims and the Buddhists when they traveled around the world.
When European countries, North and South America, South-Africa, Australia and New-Zealand colonized, traveled the cat along and set everywhere where people lived. In the 19th century the cat was on every continent, Except Antarctica.