"We chose legal action very reluctantly and only after repeatedly asking Samsung to stop copying our work," Cook said in an internal memo obtained by Reuters.
Cook's message sent to Apple employees late on Friday followed a decisive win handed to the company by a California federal court in its patent infringement battle against Samsung.
A nine-member U.S. jury found that Samsung had copied key features of the hugely popular iPhone and iPad, and awarded Apple $1.05 billion in damages.
The courthouse victory is a big blow to Google Inc
"The jury has now spoken," Cook said in the memo titled "An important day for Apple."
"We applaud them for finding Samsung's behavior willful and for sending a loud and clear message that stealing isn't right," Cook said, adding that he hopes "the whole world listens."
The verdict, seen by experts as one of the largest in patent history, came as a one-year anniversary present for Cook, who took over the CEO job from late co-founder Steve Jobs exactly a year ago. It also vindicates Cook's long-held position that the company cannot "be the developer for the world."
But Samsung warned that the San Jose court's verdict was not "the final word in this case or in battles being waged in courts and tribunals around the world." Apple, meanwhile, said it will move to block sales of Samsung's infringing devices in the United States.