The property tycoon has purchased the entire South Ayrshire complex, including the hotel, from the Dubai-based group Leisurecorp for an
undisclosed sum, but it is believed to be about £35million.
Turnberry is the only course in the Open circuit to be owned privately. The course is operated by Starwood Hotels.
As reported in The Herald earlier this week, the deal markled a U-turn for the businessman.
In February, Mr Trump indicated he had no further plans to invest in Scotland following a long-running dispute over a planned offshore wind farm.
He and his company had consistently opposed the plan, which he claimed would spoil the view from his development
at the Menie Estate, Aberdeenshire.
Mr Trump has indicated he may rename Turnberry after himself and also promised to "bring a new level of luxury" to the golf resort.
The resort includes three links courses, a golf academy and the famous five-star hotel, which dates back to 1906 and has 149 rooms.
It was owned by the Starwood chain from 1997 until 2008, when it was bought over by Leisurecorp, which is a subsidiary of the Dubai government.
Speaking for the first time about the deal, Mr Trump said buying Turnberry was too good an opportunity for him to resist. He described the resort's Ailsa course as "one of the greatest in the world," adding: "It's a special place. It's an important place"
Mr Trump, who owns 16 golf resorts around the globe, promised to bring a "new level of luxury" to the hotel, which he said was in a fabulous location.
When asked whether it would be renamed after the tycoon, Mr Trump replied: "Trump Turnberry has a nice ring to it, doesn't it? We'll make that decision fairly soon - in a couple of days."
He added: "Our aim is to make it the finest golf hotel in the world."
He said Turnberry remained one of the greatest courses in the world and he would do nothing to tamper with it without the approval of the Open organisers, the Royal & Ancient. Turnberry has hosted the Open four times.