The Northern Irishman's win in his native Belfast sets up a shot at the IBF world title held by Leeds boxer Josh Warrington.
Having successfully defended the interim WBO title, Frampton will also be confirmed as mandatory challenger to full champion Oscar Valdez.
Frampton dominated throughout the encounter in front of his home crowd as the Australian's corner eventually threw in the towel in the ninth round.
Frampton was on the front foot from the first, rocking Jackson back several times with his overhand right.
The following two rounds saw Frampton suffer a cut to his right eye from what appeared to be an accidental clash of heads, but the home favourite nonetheless remained in control.
From then on it remained one-way traffic, with Jackson receiving a pummelling in the fourth and fifth before Frampton opted to conserve energy in the latter stages of sixth.
The eighth round saw Jackson dropped with an explosive body shot and, although the Australian managed to get up and continue, his corner had seen enough come the next round.
Frampton moves to 26-1 with 15 knockouts following Saturday's victory.