The businessman flew into Aberdeen on his private jet today following his first visit to the Ayrshire resort since he announced the purchase.
The deal will close in around five weeks but Mr Trump did not reveal the price tag, and said only that he paid "a lot" for a resort which includes the Open Championship golf course.
Turnberry brings the number of golf resorts owned by the property magnate to 17.
Speaking on board his Boeing 757 jet, Mr Trump said he will spend around 200 million US dollars (£120 million) to make the Turnberry hotel "the finest in Europe", but plans only to "tweak" the renowned course - and not without the blessing of 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.
"We're going to spend a tremendous amount of money - probably about 200 million US dollars - on bringing the hotel to the highest standards of luxury.
"I think it'll be the finest hotel in Europe when it's finished."
Asked about plans for the course, he said: "Turnberry has been a great course for many years. With Turnberry, you don't talk about a redesign, you talk about tweaking. You can't do a redesign.
"I wouldn't do anything without the absolute blessing of the R&A."
Mr Trump was accompanied on his Aberdeen trip by daughter Ivanka.
It is his first visit this year to the Trump International Golf Links at Balmedie on the Aberdeenshire coast, which opened in July 2012.
Plans for a second golf course, club house and hotel are on hold amid a bitter dispute over a proposed wind farm adjacent to the resort.
Mr Trump was speaking while sitting on one of his jet's cream leather sofas, decked with velvet cushions bearing the Trump logo.
The luxury plane boasts a kitchen, a double bedroom and a bathroom with golden taps and sink.
Ms Trump, sitting by her father's side, said of Turnberry: "It is unbelievable. The building itself, the hotel, is one of the greatest masterpieces of architecture, not just in Europe, but really anywhere.
"It's really exciting, I've no doubt he'll make it a phenomenal resort."
Mr Trump said his Menie Estate course in Aberdeenshire remained "his baby", and he welcomed positive reviews in the golfing press.
He said he is ready to expand the resort as soon as the wind farm plans are dropped.
Mr Trump said: "This is my baby, I'm very proud of it. I think we might have built the best course in the world. We've been rated so well.
"As soon as they give up this charade of these terrible, destructive windmills, which are destroying Scotland, we will continue onwards.
"As soon as they stop the craziness, which nobody wants, we will get going."
Asked if he would consider pulling out of the resort if the wind turbines are built, he said: "I would say that I would be extremely unhappy and so would the people of Aberdeen.
"I would be so disappointed."
Mr Trump was met at the airport by Sandy Jones, chief executive of the Professional Golf Association.
He said: "He's never gone into a golf course and made it worse, he always makes it better.
"Turnberry is already number one, so how much better can you make it?
"But he will make it better. It's a resort that just needs that tender loving care and a bit of investment.
"Obviously it is already an Open Championship venue which I know he wanted in Aberdeen and eventually I think he will get."
Before arriving in Scotland Trump visited another new golfing property, the Doonbeg links in the west of Ireland.
The billionaire New Yorker said he plans to invest up to 45 million euro (£36 million) in the Co Clare club.
The idea is to create a golf circuit from Doonbeg to Turnberry and on to the Menie Estate - dubbed the Trump Triangle.
He said earlier this week: "We are already in contract for an incredible helicopter that will connect the three dots with guests and we think that is going to be a tremendous amount of business.''