"So well written. So thoughtful. So thoughtful."
Mr Obama left a letter for his successor in the Oval Office before departing the White House - as is the tradition from one president to the next.
He was filmed through a window leaving the envelope in the drawer during his final moments as president.
But the White House has not provided details about what Mr Obama conveyed to Mr Trump in the note.
Mr Obama campaigned vigorously against Mr Trump. But the former president and president have had regular phone conversations since the election, with Mr Obama offering guidance and advice.
"(It was) in the drawer, which is a custom, but I doubt too many of them were written in this manner," Mr Trump said.
"In fact I called him and thanked him for the thought that was put into that letter.
"It was long, it was complex, it was thoughtful, and it took time to do it and I appreciated it.
Mr Trump said there was nothing in the letter that surprised him but that "it was stated beautifully that I'm representing a lot of people".
"And I'm carrying on a very important tradition and just 'do a great job'.
"He wants me to do a great job.
"He said something that was very interesting to me.
"He said 'you know if I thought your health care plan was going to be better than his plan, Obamacare, I would support it'.
"And I believe he would."
