Campbell had scored the only goal of the first leg to give Gary Naysmith's side a slender advantage going into the second leg at Ainslie Park but it was the visitors who drew first blood, Darryl McHardy heading home the opener after 22 minutes to square the tie on aggregate.
Elgin’s lead lasted just four minutes as moments as Danny Handling nudged the Citizens back into an aggregate lead with the equaliser, slotting past Tom McHale from Craig Thomson’s cross.
Ouzy See and Callum Crane had chances for the hosts before McHardy headed Elgin back in front on the night four minutes before the interval.
City upped the tempo in the second half with Campbell, Crane, Handling, and See all going close.
But with the game looking destined for extra time Campbell unleashed an unstoppable effort that beat McHale, sealing a 3-2 aggregate win for Edinburgh City in front of Easter Road boss Ross and his assistant John Potter, who were watching from the stand.
City will meet Dumbarton in the play-off final on May 17 after the Sons beat Stranraer 1-0 after a goalless draw at Stair Park on Saturday.
Ross Forbes hit the bar with an early effort before Jaime Wilson found the net eight minutes before the break.
Ruari Paton had a chance to equalise in the second half but struck his penalty against the post, consigning Stranraer to another season in League Two.