The 37-year-old, who was invited to play alongside the politician, teed off on Sunday at a luxury golf resort in Florida.
"Playing with Mr President was pretty cool," The Telegraph quotes Woods as saying. "He's just a wonderful person to be around. And we won. There's a process that's involved and I was invited to play.
"It was an invitation that certainly you don't turn down, especially being he's an avid golfer and so am I. He has got amazing touch."
The pair went up against US trade representative Ron Kirk and Houston Astros owner Jim Crane.