The Court of Appeal ruled that, even though parts of the product look similar to Apple's iPad, the tablet does not copy its rival's design.
Apple will now have to place prominent advertisements in several UK newspapers and magazines, explaining that Samsung did not copy the iPad.
It will also have to carry a link to the judgement on the homepage of its website.
A spokesman for Samsung said the company "welcomed" the court's decision.
"We continue to believe that Apple was not the first to design a tablet with a rectangular shape and rounded corners and that the origins of Apple's registered design features can be found in numerous examples of prior art," he said.
"Should Apple continue to make excessive legal claims in other countries based on such generic designs, innovation in the industry could be harmed and consumer choice unduly limited."
Apple's appeal was dismissed by Lord Justice Longmore, Lord Justice Kitchin and Sir Robin Jacob, who said: "If the registered design has a scope as wide as Apple contends, it would foreclose much of the market for tablet computers.
"Alterations in thickness, curvature of the sides, embellishment and so on would not escape its grasp. Legitimate competition by different designs would be stifled."
The appeal followed a ruling in July that, whilst the Galaxy Tab and iPad were "very, very similar" when viewed from the front, there were significant differences in both the thinness of the tablets and the detailing on the back.
Judge Colin Birss said that Samsung's design was "not as cool" as Apple's.
The two companies are the world's leading smartphone makers and have been fighting over patents in courts around the world.
Figures show Apple sold more than 17m iPads in the third quarter of this year alone, generating revenue of $9.1bn (£5.6bn).
The company declined to comment on the Court of Appeal's decision.