The famous Ayrshire golf resort will be renamed Trump Turnberry, and £100 million has been pledged to renovate the hotel that overlooks the golf course.
Mr Trump said the deal was completed yesterday morning.
On a visit to Scotland last month the businessman did not reveal the price tag, only saying that he had paid "a lot" for the resort which includes a course on the Open Championship circuit.
It brings the number of golf resorts owned by the property magnate to 17.
Mr Trump said: "I am honoured to own and manage this magnificent property, perhaps the most exciting property there is. We will be spending a great deal of time, effort and money to make Trump Turnberry the finest resort of its kind anywhere in the world."
During a flying visit to Turnberry, and then to his course in Balmedie on the Aberdeenshire coast, in May, Mr Trump said he would only "tweak" the Ayrshire site - and not without the blessing of governing body the Royal & Ancient.
He said: "We'll bring it to a level that it's never been before.
"It's going to be spectacular. It's rated the number one course in the world and we're going to be working with the Royal & Ancient on certain things that are going to be even more spectacular.
The resort is to be owned and managed by the Trump Organization but the hotel will continue to be managed by Starwood Hotels & Resorts.
Mr Trump is to visit the course next month to discuss his plans for the resort.
A statement released today by the Trump Organization to confirm the purchase said Turnberry had "been the home of four of the greatest Open Championships of all time", including the 1977 "Duel in the Sun" where Tom Watson won over Jack Nicklaus.
Mr Trump's first Scottish course in Aberdeenshire opened in July 2012.
Plans for a second golf course, club house and hotel on the same site are on hold amid a bitter dispute over a proposed wind farm adjacent to the resort.