The Presidential Medal of Freedom (along with the Congressional Gold Medal) is the highest award that can be awarded to a civilian in the United States.
Woods, 43, completed one of the most unlikely comebacks in the history of sports with his victory at Augusta National over the weekend.
Trump didn't indicate when he'll present the medal to Woods.
Trump, an avid golfer, was photographed on the green in Florida with Woods and pro-golfer Jack Nicklaus in February.
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Trump handed out his first medals a year ago, making a posthumous award to Elvis and Supreme Court Justice Antonin Scalia and baseball legend Babe Ruth.
Yogi Berra, Billie Jean King, Muhammad Ali and Arnold Palmer are among other sports figures who have received the Presidential Medal of Freedom.
Trump's assessment then of Woods' game was spot-on, with the president predicting that Woods would "be winning majors again".
Trump spent much of Sunday at this golf course in Northern Virginia and appeared to be watching the Masters for at least part of the day, based on his Twitter posts.
"Love people who are great under pressure".
Many are calling Woods' victory a personal and professional comeback.