Slipper,(26) takes over from Stephen Moore who has been rested alongside a host of Wallabies regulars including vice-captains Michael Hooper and Adam Ashley-Cooper for Saturday's (Sunday NZT) World Cup warm up Test at Soldier Field in Chicago.
"There is no greater honour for a player than to lead his country and I am excited to be able to do it with this incredible group of players," Slipper said.
"Stephen [Moore] has done a fantastic job in bringing this group together, and I will do my best to honour him and my country when we take on the Eagles.
"We've always looked at things this season as a collective, with players being able to step up at different stages. That also applies to leadership, and we have a lot of solid leaders in the squad, which is essential in a year like this one."
Cheika named Nick Phipps and Bernard Foley in the halves while two uncapped players, prop Toby Smith and winger Taqele Naiyaravoro, are on the bench.
The clash with the Eagles comes 18 days before the Wallabies open their World Cup campaign against Fiji in Cardiff.
The bulk of the squad to face the Eagles is made up of players who need the run ahead of the World Cup with Kurtley Beale in for Israel Folau at fullback.
Gone are regular wingers Ashley-Cooper and Drew Mitchell, with Joe Tomane and Rob Horne coming in, while Henry Speight takes over at No 13 from regular outside centre Tevita Kuridrani.
Will Genia will make his return from knee surgery off the bench, with the veteran halfback set to play his first game since the Rugby Championship opener against South Africa in July.
Inside centre Matt Giteau and No 6 Ben McCalman are the vice-captains for the match.
"James led well at Queensland this season, and is an important leader in our squad. This test match against the USA will give him the honour of captaining his country and the opportunity to lead from the front," Cheika said.
"We are working hard to develop our leaders and James along with Matt Giteau and Ben McCalman, who lead by example both on and off the field, will make up a strong leadership team."
McCalman is the blindside flanker with Sean McMahon the openside, while Wycliff Palu gets a much-needed hitout at No 8 with Hooper and David Pocock rested.
Tatafu-Polota-Nau returns to the starting lineup at hooker, joining lock Kane Douglas in his first run-on Test of the 2015 international season.
Three players on the bench - Naiyaravoro, Sam Carter and James Hanson - are not even in the Wallabies' 31-man World Cup squad.
Wallabies team: Kurtley Beale, Joe Tomane, Henry Speight, Matt Giteau, Rob Horne, Bernard Foley, Nick Phipps, Wycliff Palu, Sean McMahon, Ben McCalman, Rob Simmons, Kane Douglas, Greg Holmes, Tatafu Polota-Nau, James Slipper (capt). Reserves: James Hanson, Scott Sio, Toby Smith, Dean Mumm, Sam Carter, Quade Cooper, Will Genia, Taqele Naiyaravoro.
