The Ryder Cup will be played Sept. 28-30 at Le Golf National outside of Paris. The U.S. has not won in Europe since 1993.
The appointments are in keeping with the continuity the U.S. team sought following a 2014 defeat, the Americans' third in a row.
Furyk had already appointed 2012 and 2016 captain Davis Love III to be a vice captain. Furyk and Love, along with Woods, served as assistants on Stricker's winning U.S. Presidents Cup team last year and this will be Stricker's third time as a Ryder Cup vice captain. He will also be a strong candidate to be the captain of the 2020 team when it plays in his native Wisconsin.
Woods was an assistant for the U.S. Ryder Cup victory at Hazeltine in 2016. When asked last week at the Genesis Open about the possibility of being a player or an assistant, Woods said, "Why can't I do both?''
Furyk acknowledged the possibility of Woods playing on the team and Woods said in a statement, "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."
The top eight players in a points system will automatically make the team, with Furyk getting four at-large picks.
European captain Thomas Bjorn has so far named Robert Karlsson as one of his vice captains.