The 25-year-old became the first boxer to stop Martinez with a right hand on Saturday night.
The referee gave the 26-year-old Spaniard the chance to fight on after he hit the canvas in the ninth, but Martinez was unable to continue as he stumbled towards the ropes.
Earlier Frampton looked comfortable in a cagey first round, but Martinez upped the tempo in round two with a number of body shots.
A powerful left hook from the defending champion caught Frampton off-guard in the fourth round.
Frampton hit back before assuming control progressively and ending the fight in style in the ninth, as Martinez failed to derail his World title hopes.
The Tiger's Bay boxer, who is undefeated as a professional boxer, celebrated with manager Barry McGuigan and trainer Shane McGuigan after the fight.
"It feels amazing," he said. "I just want to thank everyone who came out here. I just want the whole of Belfast to be proud of me. I want to be a world champion and I'm getting close."
(Martinez)'s a big, big puncher. People had doubts about my chin. It just shows I've got a solid chin.
The Spaniard had pulled out of the contest twice in the last 18 months, blaming internal issues in his camp for the delays.
There were heated exchanges between the boxers during a press conference ahead of the much-anticipated fight. Martinez also made throat-slitting gestures towards his challenger at the weigh-in.
But Frampton played down the tension between the pair.
"(It was a) very tough night. He was harder to hit than I thought. He's tough as nails," he said.
"All that stuff at the weigh-in - that's just macho-ism. He's a nice guy and I'll shake his hand.
"I told him I'd outbox him at the start and I'd outfight him at the end - and that's exactly what I've done.
"He's one of the hardest fighters in the super-bantamweight division and I could take him all day."