A healthy lead from the first leg was more than enough for the 2010 quarterfinalist to book a place in Brazil.
The Black Stars boasted a 6-1 advantage from their meeting in October and were never in serious danger of being upset. Amr Zaki gave the home side slight hope with a first-half goal but no further inroads were made until the closing stages, when Gedo struck. With seconds of the game left, the visiting team pulled one back through Kevin-Prince Boateng.
The comprehensive 7-3 aggregate win means Ghana has qualified for its third consecutive World Cup, while Egypt has not made the finals since 1990.
Egypt played in front of its home fans for the first time in almost two years following the Port Said riots and ousting of President Mohammed Morsi. Supporters had been banned from attending effectively all club and international games since the riots, which saw more than 70 fans killed in a match between Al Ahly and Al Masry in February 2012.
Bob Bradley made five changes to the side that crumbled to a 6-1 defeat in the first leg, with Zaki, Kahraba and Ramy Rabia among those to come in, while Harrison Afful replaced Samuel Inkoom in the only Ghanaian alteration from the opening encounter.
Zaki let fly from the edge of the penalty area in the opening minutes, but fired his effort straight at Ghana goalkeeper Fatau Dauda.
Rashid Sumaila then went close to dashing Egypt's slim qualification hopes after six minutes when he drilled a low effort narrowly wide of the target from 18 yards.
But it was Egypt which took the lead in the 25th minute when Zaki bundled over the line from close range after Dauda failed to deal with a Mohamed Aboutrika free kick from the right.
Ghana's players were subjected to a barrage of distracting laser pens as the home fans tried to play their part in influencing an unlikely comeback, and Egypt continued to have the better of the chances - an inspired Zaki forcing Dauda to tip over from distance 10 minutes prior to the break.
The home side maintained a high tempo for the remainder of the opening period, but was unable to breach the Ghanaian defense, leaving the team in need of five second-half goals.
Mohamed Salah tried to curl in an effort from the edge of the penalty area shortly after the interval, but sent the ball high and wide of the target.
As time ticked away, Egypt looked decreasingly likely to reduce the deficit as Ghana became content to defend the aggregate advantage.
Sulley Muntari went close to leveling the encounter on the night in the 63rd minute, but his low strike whistled beyond the post and was one of few chances in second period.
With the result already beyond doubt, Jerry Akaminko was forced to clear off the line for the visiting side after a penalty-area scramble in the 75th minute.
Gedo drilled home a second for the home side from close range in the 83rd minute only for Ghana's qualification party to start among the team's fans one minute from time as Boateng tapped home from an Asamoah Gyan cross.