"We're all excited to see him healthy again and playing well," said Furyk over Woods, who missed most of the 2016 and 2017 seasons with a long-term back injury.
"It's an advantage in our cap that plays on our side," added Furyk.
Woods, who has not played a Ryder Cup since 2012, revealed that he had set himself the goal of joining the US team. UU At the beginning of the season.
"I have not been part of the team playing for six years," said the 42-year-old, who will play his eighth Ryder Cup.
"I served as vice captain a couple of years ago, and that was incredible, this year having the honor of being able to play again is more than special," added the main winner on 14 occasions.
"At the beginning of the year, that was one of my goals, to form this team." I received Jim's call and he asked me if I would serve as vice-captain and I said, "Absolutely."
"But deep down I wanted to be part of the team, I really wanted to keep playing, it was a goal for the end of the season and, as the year progressed, I was able to somehow get some good results and that's it." I'm in the team. It's amazing, beyond the special. "
Mickelson and DeChambeau completed the other two captain selections announced by Furyk on Tuesday.
The captain of EE. UU He will announce his last place in the defending champion team next week, with Tony Finau considered the favorite for the position.
There had been little suspense around Furyk's announcement.
Mickelson was always considered a likely option for what will be a 12th appearance in the Ryder Cup.
The 48-year-old reminded Furyk of his quality with a dazzling eight-under-par 63 in the final round of the Dell Technologies Championship on Monday.
"Being able to play at that elite level for as long as he has, being so consistent during all the time he has is an impressive feat," Furyk said of Mickelson.
"I'm excited to have him on the team, he's a veteran leader, he knows the inner workings of our team room and it provides a spark, it's great to have him as a part of it."
The United States will seek its first victory in the Ryder Cup on European soil in 25 years when they face Europe at Le Golf National in Saint-Quentin-en-Yvelines, just outside of Paris.
Mickelson said ending the long wait for the United States for a victory in Europe was his main motivation.
"It's obvious that the only thing that has been lost in recent years is that our team goes to Europe and wins," said Mickelson.
"I'm very excited about the team this year, we have some incredible players, great leadership and a really special opportunity to do something we have not done in a long time.
"It's a wonderful opportunity to do something I did not do in my career and I would like it very much."
DeChambeau, 24, had practically been guaranteed one of the captain's selections after breaking into the first two legs of the PGA Tour FedEx Cup tiebreaker series, winning the Northern Trust and the Dell Technologies Championship.