Woods, who made his comeback in January after recovering from spinal fusion surgery in 2017, will take the role for the second time in his career.
The announcement, which was made by team captain Jim Furyk at a recent press conference, has left Woods "excited" about the season ahead.
"The Ryder Cup is incredibly special to me," the 42-year-old said. "I am thrilled to once again serve as a Ryder Cup vice-captain and I thank Jim for his confidence, friendship and support.
"My goal is to make the team, but whatever happens over the course of this season, I will continue to do what I can to help us keep the Cup. I'm excited about the challenge ahead."
Furyk added that the partnership between Woods and Stricker will give the USA team an "invaluable resource" heading into the Major.
"To win in Paris will be a great challenge, and to have Steve and Tiger share in the journey is important for me and for American golf," he said. "The deep appreciation they both have for competition, the concept of team, and the Ryder Cup is infectious. Their knowledge and experience will be an invaluable resource in our effort to retain the Ryder Cup."
This year's Ryder Cup kicks off at the Le Golf National course in the French capital.