The ruling follows a July 9 London court decision that Samsung's Galaxy tablets don't infringe Apple's registered designs.
Judge Colin Birss said that the climb down should be posted on Apple's UK home page for six months and published in several newspapers and magazines.
The idea, said Judge Birss, was to correct any impression the South Korea-based company was copying Apple's product. Birss famously ruled that no one could confuse Samsung's tablet with Apple's design because it "was not cool enough".
This might be a bit tricky for Apple, as it is still fighting Samsung in several other courts throughout the world, so an admission on its UK website might stuff up its cases somewhat.
It means that Apple will have to publish "an advertisement" for Samsung, and no company likes to refer to a rival on its own website.
But Birss declined to grant Samsung's bid for an injunction blocking Apple from making public statements that the Galaxy infringed its design rights.
He said that Apple was entitled to its opinion, even if, in this case, it was wrong.
As well as Apple's website, the company must pay for notices in the Financial Times, the Daily Mail, Guardian Mobile magazine, and T3.
Apple's lawyer said the company would appeal the July 9 decision so we will not see the adverts for a while yet.