An emotional Woods thanked those in attendance at the Rose Garden ceremony at the White House for their support through the years when he was not winning.
"You've seen the good and the bad, the highs and the lows, and I would not be in this position without all of your help," he said after Trump placed the medal around his neck.
Woods recalled his breakthrough triumph at Augusta 22 years ago which the then 21-year-old celebrated with his father and mentor Earl, who died in 2006.
"In '97, yes, I won the Masters and I ended up hugging my dad and my mom," he said.
"My dad is no longer here but my mom is here, I love you mom," he added, his voice cracking with emotion as he went on to thank his two children and girlfriend Erica Herman.
"The amazing Masters experience I just had a few weeks ago certainly is part of the highlight of what I've accomplished in my life on the golf course."
Trump, an avid golfer, described the 15-times major champion as a "a global symbol of American excellence, devotion and drive".
Woods joined Arnold Palmer, Charlie Sifford and Jack Nicklaus as the only golfers to have received the award.
It is awarded annually to people who have made outstanding contributions to the security or national interests of the country, to world peace, or to cultural or other significant public or private endeavours.
Since taking office Trump has given the award to several athletes, including former professional NFL players Roger Staubach and Alan Page as well as posthumously to baseball great "Babe" Ruth.
(Reporting by Rory Carroll, editing by Nick Mulvenney)
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