World number 12 Gaudio and number 20 Moya have shoulder injuries, the All England Club said on its website on Monday as it issued the final entry lists for this month's Championships.
Gaudio, who claimed the French title in 2004, is replaced by Janko Tipsarevic of Serbia and Montenegro while Moya, who won at Roland Garros in 1998, is replaced by CzechBohdan Ulihrach.
The 2002 French Open champion Costa, who has slipped to 84th in the world rankings, has undergone knee surgery and will be replaced by Australian Scott Draper.
Wimbledon organisers also confirmed the withdrawals of American Mardy Fish (wrist injury) and Argentines Mariano Zabaleta (foot) and Juan Ignacio Chela.
The seedings for the June 20-July 3 grasscourt grand slam tournament will be announced on Wednesday with the draw on Thursday.