Ghana-born Adu joined Major League Soccer at age 14 in 2004 as a highly touted prodigy, becoming the youngest US pro athlete in 115 years. But Adu struggled over the past four years with European clubs in France, Portugal, Greece and Turkey, before making a US comeback at 22.
Shea and New York's Juan Agudelo are joined among USA's major names by Terrence Boyd of Borussia Dortmund and Joe Gyau of Hoffenheim and Kansas City's Teal Bunbury.
The only non-MLS defender picked for the lineup, which is limited to players 23 and under, was Josh Gatt of Norwegian side Molde. The right back missed an exhibition game and training camp last month due to an ankle injury.
"This roster is a culmination of a long process to select what we feel is the best team this country has to offer in the U-23 age group," coach Caleb Porter said.
"I feel very confident in this collection of players and their ability to execute the playing style we believe will best represent their talents and get us to London."
The Americans are in CONCACAF qualifying group A along with Cuba, Canada and El Salvador for home-soil matches in Nashville, Tennessee on 22-26 March with Mexico, Honduras, Panama and Trinidad and Tobago in group B at Los Angeles.
The two top teams from each group advance to the semi-finals on 31 March at Kansas City and the winners of those two matches will advance to the London Olympics.
"This is a tremendous opportunity for these young players," US national team coach Jurgen Klinsmann said. "Playing the Olympic Games is a once-in-a-lifetime chance, and we are fully supporting their efforts to qualify."