The United States businessman's organisation brought Doonbeg resort from the receivers.
Mr Trump issued a statement revealing the resort would be renamed the Trump International Golf Links, Ireland.
He said Doonbeg was an already terrific property that would soon be unparalleled and have the highest standards of luxury.
Speaking from New York later, Mr Trump said he was switching his focus to Ireland after a Scottish judge rejected his legal action against a wind energy project off the Aberdeenshire coast, which he claimed would spoil the view from his luxury golf course there.
"We will appeal this decision, and in the meantime we will be focusing all of our investment and energy towards our new acquisition on the Atlantic Ocean in Ireland," he said.
American billionaire Donald Trump has bought a  golf resort in County Clare in the Republic of Ireland.