Bedoya is expecting the birth of his second child next week.
The U.S. plays its quarterfinal Wednesday in Philadelphia against a third-place team from another group, likely Honduras, El Salvador or Jamaica. The opponent was to be determined Sunday night.
Using a mostly junior varsity group, the Americans opened with a 1-1 tie against Panama and wasted a two-goal lead against Martinique before winning 3-2. The U.S. defeated Nicaragua 3-0 Saturday night, getting an 88th-minute goal from Matt Miazga to win Group B by edging Panama based on total goals.
Each team is allowed to make up to six changes in the 24 hours after finishing the group stage, and the additions must come from the 40-man preliminary roster submitted in early June.
"We have added some experienced players," Arena said in a statement. "The players leaving all made a good impression, and I'm optimistic for their future with the national team program."
Dempsey has 56 international goals, one shy of Landon Donovan's American record. Dempsey, Bradley, Howard and Altidore all are regular starters when the full national team player pool is called in, and Nagbe appeared in the first seven U.S. matches this year after Arena replaced Jurgen Klinsmann and started his second stint as coach.
The U.S. improved to 32-1-4 during the group stage of the Gold Cup and 6-0-5 since Arena returned.
The revised roster:
Goalkeepers: Jesse Gonzalez (Dallas), Bill Hamid (D.C.), Tim Howard (Colorado)
Defenders: Matt Besler (Kansas City), Omar Gonzalez (Pachuca, Mexico), Matt Hedges (Dallas), Eric Lichaj (Nottingham Forest, England), Matt Miazga (Chelsea, England), Justin Morrow (Toronto), Jorge Villafana (Santos Laguna, Mexico), Graham Zusi (Kansas City)
Midfielders: Kellyn Acosta (Dallas), Paul Arriola (Tijuana, Mexico), Michael Bradley (Toronto), Joe Corona (Tijuana, Mexico), Dax McCarty (Chicago), Darlington Nagbe (Portland), Chris Pontius (Philadelphia), Gyasi Zardes (LA)
Forwards: Juan Agudelo (New England), Jozy Altidore (Toronto), Clint Dempsey (Seattle), Jordan Morris (Seattle)