Although Woods has plummeted in the world rankings due to his inactivity, and even though he has not played well in limited action, Couples said he wanted Woods on the 12-man squad.
Couples was originally scheduled to announce his two captain's picks Sept. 26.
"There's no reason for me to wait until Sept. 26 to pick Tiger," Couples said. "He's the best player in the world forever."
Woods is too far back on the points list to qualify for one of the 10 automatic spots to the team. He has appeared in only eight events this season.
"Is he playing well right now, no," Couples said. "He almost won Augusta (the Masters) three or four months ago, so you don't do that by playing poor golf."
Among the players who have yet to automatically qualify are PGA Championship winner Keegan Bradley, Rickie Fowler and Jim Furyk.
Those currently in the Top 10 on the qualifying points list are Phil Mickelson, Steve Stricker, Hunter Mahan, Bubba Watson, Webb Simpson, David Toms, Bill Haas, Matt Kuchar, Nick Watney and Dustin Johnson.
The United States will take on a team of international players in the Presidents Cup matches scheduled to begin Nov. 17 in Melbourne.
Couples made the announcement at the site of the Boeing Classic, a Champions Tour event that starts Friday.