Floyd, America's 1989 captain and an eight-time Ryder Cup player, will serve as vice-captain for the second time after also assisting Paul Azinger in 2008.
He is the second vice-captain selected by Watson, joining two-time US Open winner Andy North.
Watson told pgatour.com: "You look at Raymond's eyes, you never saw his eyes waver. No matter if he was shooting 80 - which he rarely did - or shooting 65, his eyes had a focus that you like to see.
"The way he played the game was every shot counted, and that's the type of guy that I want to be taking care of my back, as the captain."
Floyd thanked Watson for selecting him and said of his role: "Tom is the captain and he, and we as vice-captains, don't hit a shot.
"Our responsibility is to see that these guys are comfortable, that they are happy. We need to be an uplifting spirit, if you like.
"Any questions these guys have, they have to be comfortable to come to us."
Watson agreed: "We set the stage for these players to go compete. They have to go out and they have to act.
"In my opinion, (Floyd) couldn't be a better person from the standpoint of the respect of the players because he's been there.
"He'll have stories to share and he'll have an understanding of what the pressure is like. He'll be able to relate to the players and be there for them. He'll be able to see how nervous they get and talk to them from the standpoint of 'this is how I did it'."
There will be no shortage of experience in the American camp as Watson, Floyd and North go into the match, which begins on September 26, with a combined age of 201.
North will be 64 next month while September 4 is both Watson's 65th birthday and Floyd's 72nd.
Watson previously captained the States in 1993, when he selected a then 51-year-old Floyd as one of his two wild cards.
That made Floyd the oldest player in Ryder Cup history, and he justified his captain's faith by winning three of his four matches.
Watson's picks on that occasion were made on the basis of form leading into the tournament and he plans to use the same approach for his three picks this time around.
"In '93, I had two picks and throughout late spring and the summer, the guys on the borderline (of automatic qualification) were not playing well," he said. "They were missing cuts, and when they were making cuts they were finishing 50th.
"I said 'I want to go with someone who's playing well, they need to have a good stretch of golf going'.
"I'll look at it the same this year, I'll look at someone who's lighting it up, who's making putts - they'll be first on my list.
"I'll find that out through my contacts, and that's going to be a crucial element in how I pick my team.
"Those players who get on the team are going to be the best possible players we can have on the team and if they perform, we'll win."