He has purchased the entire South Ayrshire complex, including the hotel, from Dubai-based group Leisurecorp for an undisclosed sum.
In a statement, Mr Trump said it was "an honour and privilege to own one of golf's greatest and most exciting properties".
The course will continue to be managed by Starwood Hotels & Resorts.
Turnberry is the only course in the Open circuit to be owned privately. Mr Trump has ambitions to host the Open at his other course in Aberdeenshire.
In a statement, Mr Trump said: "I intend to invest many millions of dollars (pounds) in order to bring the hotel to the highest levels of luxury.
"When completed, I believe that the Turnberry Hotel will be the finest and most luxurious hotel in all of Europe."
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.
When the Aberdeenshire plan was approved, Mr Trump said: "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."
His campaign against the wind farm included an open letter to First Minister Alex Salmond.
In it he said: "Taxing your citizens to subsidise wind projects owned by foreign energy companies will destroy your country and its economy.
"Jobs will not be created in Scotland because these ugly monstrosities known as turbines are manufactured in other countries such as China.
"These countries are laughing at you."
In his response, Mr Salmond said he was "determined that communities across Scotland will benefit directly from offshore wind, which is forecast to generate about Â£30bn of investment and lead to the creation of up to 28,000 Scottish jobs".
Turnberry has hosted the Open Championship four times, most recently in 2009.
That year, it was won by Stewart Cink of the United States.
It has also been the venue for the Senior's Open and the Women's British Open.
The golf resort comprises three courses, a hotel, self-catering accommodation and a spa.
Its official website claims it was the first purpose-planned golfing resort in Britain.
US property tycoon Donald Trump has confirmed that he has bought the Turnberry golf resort.