In a hand-written letter addressed to Rao, she described her visit as an "incredible and inspiring experience".
Ivanka Trump had led a delegation of US administration officials and entrepreneurs at the Global Entrepreneurship Summit (GES) held in Hyderabad in November.
Prime Minister Narendra Modi also hosted a gala dinner for her at the famous Falaknuma Palace Hotel in the city.
Ivanka Trump, in her letter to the chief minister, said she was touched by the warmth of the people of Telangana.
"I also want to thank you for the exquisite gift that you presented to me at the Falaknuma Palace. I am deeply touched by your thoughtful gesture and by the warmth of the people of Telangana," she said in the letter, a copy of which was released on Monday.
She further said that she looks forward to coming to India in the near future. Ivanka Trump, who is also an entrepreneur, was invited by the prime minister during his visit to the White House in June to speak at the GES.