Rats in Europe have a long history tied to human travel, ports, and settlements.
If you are asking when did rats get to Europe, black rats arrived first, likely in antiquity, while brown rats reached Europe much later and then replaced them in many places.

Black rats, also called Rattus rattus or ship rats, reached Europe by antiquity.
Brown rats, Rattus norvegicus, also known as Norway rats or common rats, appeared much later and spread fast through cities and ports.
The Short Answer

Black rats arrived in Europe first, probably by the Iron Age and certainly by Roman times.
Brown rats came centuries later, likely in the early modern period, and then became the dominant urban rat in much of Europe.
Black Rats Arrived In Antiquity
Archaeologists have found Rattus rattus in Mediterranean Europe by the fourth to second centuries BC, including Corsica and Pompeii.
Later remains turned up in London and York, showing rats moved with trade, ports, and Roman expansion.
Brown Rats Reached Europe Later
Rattus norvegicus appeared in the medieval and post-medieval record.
Today, the brown rat, also called the sewer rat, Norway rat, or common rat, has displaced black rats across much of temperate Europe.
What Archaeology And Ancient DNA Show

Bones gave the first clue, and ancient DNA helped tighten the timeline.
Skeletons and genetic signatures show that rats in Europe spread in more than one wave, closely linked to shifting human settlements and trade.
Skeletons And Ancient DNA Analysis
Archaeologists found black rat skeletons from Roman-era sites, which pushed the arrival date earlier than previously thought.
With ancient DNA analysis, researchers matched bones to species and traced how rat populations expanded, disappeared, and returned.
The University Teams
A major ancient genetic study brought together researchers from the University of York, the University of Oxford, and the Max Planck Institute for Evolutionary Anthropology in Leipzig.
They used specimens from archaeological sites across Europe and North Africa to track the spread of rats through time.
Genetic Signatures Reveal Two Waves
The DNA showed two distinct waves of black rat spread.
The first wave matched the Roman world, and a second wave appeared in the medieval period, which fits the rise of renewed long-distance trade and urban growth across colonised Europe.
How Human History Helped Rats Spread

Rats followed people, cargo, and buildings, not open countryside.
When trade networks grew, rats found more food, shelter, and transport, which made them classic human-commensal species.
The Roman Empire
The Roman Empire created dense cities, grain stores, roads, and sea routes.
The Roman economic system moved goods across huge distances, and rats moved with those goods.
Decline After Rome And Return In The Middle Ages
After Rome weakened, black rats declined in many places.
During the medieval period, especially across the Middle Ages, rats returned as towns revived and trade routes thickened again.
Life Along Trade Routes
As human commensal species, rats thrive around grain, waste, cargo, and ships.
Their history mirrors ports, caravans, and urban growth more than any natural migration route.
Why Brown Rats Took Over Later

Brown rats were bigger, more aggressive, and better able to exploit sewers, basements, and urban infrastructure.
They arrived into a Europe already shaped by dense cities, so they found ideal conditions to spread quickly.
From Ships To Sewers
Rattus norvegicus adapted especially well to dirty, built-up environments.
This species became the classic sewer rat.
Invasive rats like this one spread efficiently through ports and drainage systems, and later through city sewers, where sewer systems gave them cover and food.
John Berkenhout, Charles Dickens, And The Norway Rat Name
The name “Norway rat” is misleading, since the species is not native to Norway.
Writers such as John Berkenhout helped popularize the name, and Charles Dickens later used it when brown rats were becoming familiar urban pests.
From Wild Rats To Laboratory Rats
Brown rats started many laboratory rat lines, including albino rats and other selectively bred strains.
Humans shifted wild rats to laboratory rats after centuries of contact.
The smaller house mouse, Mus musculus remained a separate domestic companion.