The Presidents Cup, which pits a team from the United State against an International squad, will be played Sept. 26-Oct. 4 at Liberty National Golf Club in Jersey City, N.J.
Hoffman will be making his first appearance in a team event.
Mickelson is 15th in the U.S. Presidents Cup standings and the top 10 automatically qualify. Mickelson finished in a tie for sixth at the Dell Technologies last week, which is why Stricker selected him over Brian Harman, Jason Dufner and Gary Woodland, who placed 12th, 13th and 14th in the U.S. standings.
"It means a lot to me this year because the players and the captains wanted me on the team even though I didn't get the spot on my own," Mickelson, 47, said, according to USA Today. "I really love being around these guys. I respect and know how great these guys are. And this team is a special team."
"Phil brings a wealth of experience to the team," Stricker said. "He struggled a little bit at the end of the year but he showed his desire and effort to make the team and he had a great showing in the Dell Technologies Championship. From reports from the players, that was the Phil of old."
Stricker called the selection of Hoffman, who is 11th in the standings, was a "no-brainer," since Hoffman has won four PGA Tour titles this year to go along with seven top-10 finishes.
Mickelson and Hoffman join the 10 automatic qualifiers: Dustin Johnson, Jordan Spieth, Justin Thomas, Daniel Berger, Rickie Fowler, Brooks Koepka, Kevin Kisner, Matt Kuchar, Patrick Reed and Chappell.
Internationals captain Nick Price selected Emiliano Grillo and Anirban Lahiri, who is 16th in the International Presidents Cup standings, as his at-large picks. Grillo had a final-round 66 in the Dell Technologies Championship to move into the 11th spot in the standings.
Those two join the 10 automatic qualifiers for the International team: Hideki Matsuyama, Jason Day, Adam Scott, Louis Oosthuizen, Charl Schwartzel, Marc Leishman, Branden Grace, Jhonattan Vegas, Si Woo Kim and Adam Hadwin.
The U.S. leads the series 9-1-1, losing only in 1998.