Mickelson, who has played on every Presidents Cup team since 1994, used last week's Dell Technologies Championship in Boston to argue his case when he posted four sub-70 rounds to finish six shots back of victor Justin Thomas.
"We all know what Phil brings to the table", 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".
Worldwide team captain Nick Price filled out his squad by naming Argentina's Emiliano Grillo and India's Anirban Lahiri to a team that has defeated the United States just once since the competition began in 1994.
The International Team has not won a Presidents Cup since 1998 and has lost six in a row after a tie in 2003.
The matches start September 28 at Liberty National in New Jersey, where Mickelson has a corporate membership.
"I've had my eye on the 11th spot as it came down to a tight race between two very talented players".
The surprise was global captain Nick Price taking Lahiri, who missed a short putt on the 18th hole in 2015 that proved pivotal in the Americans winning.
"We felt we wanted some players who played the USA tour the whole time, " Price said.
For Mickelson, already a member of the World Golf Hall of Fame with 42 career PGA Tour wins, his addition to the team means he will have played in 23 consecutive team matches for the United States, including the Ryder Cup, dating back to 1994.
This is the first time since 2007 that every player on the worldwide team has a full PGA Tour card.
After a lackluster summer, including missed cuts at The Open and the PGA Championship, Mickelson's status was in doubt, even with all his experience and back-room influence.
Stricker seemingly just wanted some show of form to make the pick.
"People will rally behind him no matter where he's at, " Stricker said.
Plus, Mickelson's biggest support comes from the NY area, and he's a favorite in the team room. "But he's like a favorite son there".