Under the terms of the deal, Apple Inc will own all rights to the Apple brand for its products and the Apple iTunes service. Apple Corporation will license back some Apple brands where needed.
"We love The Beatles and it has been painful being at odds with them over these trademarks," said Apple chief executive Steve Jobs.
"It feels great to resolve this in a positive manner, and in a way that should remove the potential for further disagreements in the future."
The settlement may also be a precursor to seeing The Beatles on iTunes. No records by the Fab Four have yet appeared on any music download service.
Neil Aspinall, manager of Apple Corporation, said: "It is great to put this dispute behind us and move on.
"The years ahead are going to be very exciting times for us. We wish Apple Inc every success and look forward to many years of peaceful co-operation."
Microsoft receives a 30 per cent cut of all purchases on the Xbox digital store
Credit card thieves used Apple ID accounts to buy and sell virtual currency for Clash of Clans and Clash Royale and Marvel Contest of Champions
$5.1bn fine further evidence that the EU is anti-US, claims Trump
New cable will connect Virginia to France