Established U.S. skipper Carlos Bocanegra was not selected in the squad that will face Costa Rica in Denver on Friday and Mexico at the Azteca Stadium on Tuesday, and goalkeeper Tim Howard, who was captain in the February defeat to Honduras, is also missing due to a back injury, forcing Klinsmann to make a change.
"Clint is one of our most experienced players and ready to assume a more vocal leadership role," said Klinsmann in comments released by the U.S. Soccer Federation.
"He has been huge for us in World Cup qualifying so far and is already one of our key leaders. We know he will do a great job for these two important games," added the former Germany striker and coach.
Texan Dempsey has made 92 appearances for his country, but has worn the armband only once, taking over the role in the second half of the United States' 0-0 draw against Colombia on October 12, 2010.
The only other serious contender for the captain's role would have been AS Roma midfielder Michael Bradley, son of previous U.S. head coach Bob Bradley, but at just 25-years-old, he is five years Dempsey's junior.
The United States are one of six teams battling for three automatic qualification slots from the CONCACAF region along with Honduras, Jamaica, Panama, Costa Rica and Mexico.
(Reporting by Simon Evans in Denver, Editing by Gene Cherry)