Woods is recovering after undergoing back surgery and will miss next week's Masters in addition to several other tournaments.
The 14-time major winner is not likely to qualify for the 2014 event at Gleneagles due to form, but was set to feature as one of Watson's three captain's picks.
And that was confirmed on Friday as Watson decided to quell months of speculation regarding Woods' involvement.
"I've been asked a little bit about: 'What if he doesn't make the team?'" Watson said.
"I'll pick him for the team. I just hope he gets well and starts to play again without pain. That's all that matters.
"Everybody's been in pain before, every golfer. For some, it's ended their careers. For others, they've beat it and corrected with surgery.
"Obviously, I hope that he can recover and again swing the club without any pain."
The United States have lost the last two Ryder Cup events and have not won on foreign soil since 1993.