Gilchrist was in danger of missing Australia's first practice match against Zimbabwe on March 6 after being given permission to stay at home and be present for the birth.
Cricket Australia said in a statement on Saturday that Gilchrist's wife had given birth to a son, named Archie, on Friday.
The statement said Gilchrist would not fly to the Caribbean with the rest of the squad on Wednesday but he would join them in time for the first warm-up game.
Australia's first World Cup match is against Scotland on March 14.
"As planned, Adam will spend a few days with his family before travelling to the Cricket World Cup and will not depart with the main squad," the statement said.
"Adam should arrive in the Caribbean shortly before Australia's first practice match and will be available for selection for the entire 2007 ICC Cricket World Cup."
