Watson said he would use one of his captain's picks on Woods if the 14-times major champion failed to secure an automatic berth to the 12-man team for the biennial event through his US PGA Tour results.
"He's the best player maybe in the history of the game. He brings a stature to the team unlike maybe any other player," Watson told a news conference after being named captain for the 2014 matches against Europe in Gleneagles, Scotland.
"If he's not on the team for any unforeseen reason, and I'm sure he will be, you can bet he'll be number one on my pick list."
Relations between the two were strained a few years ago in the aftermath of the startling revelations surrounding the breakdown of Woods's marriage.
In a January 2010 television interview, Watson described the player's numerous extramarital dalliances as "bad for our game" and "something he needs to get control of."
Watson also criticized Woods's on-course temper tantrums.
"His swearing and his club throwing ... should end. That's not part of what we want to project as far as the professional golf tour is concerned," Watson said at the time.
Woods apparently does not harbor a grudge and sent his congratulations just moments after Watson was named captain, indicating no hard feelings between the two.
"I'd like to congratulate Tom Watson on his selection as Ryder Cup captain. I think he's a really good choice," Woods, who has a career 13-17-2 mark in Ryder Cup play and was 0-3-1 in last September's matches at Medinah, said in a statement.
"Tom knows what it takes to win, and that's our ultimate goal. I hope I have the privilege of joining him on the 2014 United States team."
Watson said Woods could be a key factor in U.S. efforts to end Europe's recent run of seven victories from the last nine Ryder Cup competitions.
"My relationship with Tiger is fine," Watson said.
"Obviously there's nobody else in the golf world who wanted to win more than Tiger, and he did it for so many years. He dominated this sport unlike anybody in the history of the sport. So I want him on my team."