He told a news conference he had formally given "complete and total" control to them in a bid to avoid conflicts of interest.
Mr Trump's lawyer said the President-elect had "isolated" himself from his businesses.
Sheri Dillon said Mr Trump wanted to be clear that he was not using his presidency for his personal benefit.
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Speaking at Mr Trump's first news conference since he was elected in November, Ms Dillon explained that all of the Trump Organization's businesses would be transferred to a trust controlled by his sons and the chief financial officer, Allen Weisselberg, before Mr Trump takes power on January 20.
"Together, Don, Eric, and Allen will have the authority to manage the Trump Organization and will make decisions for the duration of the presidency without any involvement whatsoever by President-elect Trump," said Ms Dillon, whose firm Morgan, Lewis and Bockius has been instructed by Mr Trump to draw up a structure to keep his business interests separate.
Ms Dillon added that an ethics adviser would be appointed to the management board of the trust to oversee any potential conflicts of interest.
No new foreign deals will be made during Mr Trump's presidency, according to Ms Dillon, and domestic deals will be subject to a "rigorous vetting process".
And she said the group has cancelled more than 30 pending deals in recent weeks, in order to avoid potential conflicts of interest.
Earlier in the news conference Mr Trump said he had rejected a $2bn deal in Dubai last weekend, demonstrating he was putting his business activities behind him.
Previous presidents have relinquished control of their business assets by putting them into what is known as a blind trust, run by independent trustees.
Mr Trump spoke last year about dealing with his holdings in this way. However, he then questioned whether it would be a blind trust if his children were in charge of the company.
His daughter Ivanka, whose husband has been named as a senior adviser to the President-elect, will not be involved with the Trump Organization in the future, said Ms Dillon.
US President-elect Donald Trump says he is handing over his business empire to his sons, Donald Jr and Eric.