Makabu was installed as the bookies' pre-bout favourite, but Bellew wasted little time in dispelling those predictions.
Bellew produced a bevy of combinations in the third round once he sensed he had hurt Makabu.
The 28-year-old from the Democratic Republic of Congo is renowned for his counter-punching abilities, but had no answers once Bellew unloaded his full arsenal in the third round.
Makabu had produced almost the perfect start in the opening round, lulling Bellew into one of his customary traps, soaking up a host of shots before countering with a straight left hand.
That clean shot put Bellew to the canvas, leaving the Liverpool native's trainer David Caldwell telling him "you got greedy" after the first round.
Both men adopted a more circumspect approach in the second round, both bleeding from their noses after trading hefty blows. But when Bellew hit full tilt in the very next round, Makabu could offer no defence.
Bellew toasted victory by launching Everton football chants to the adoring crowd, before challenging IBF and WBA cruiserweight champion Denis Lebedev to a unification fight.
Bellew warned the Russian he will have to come to England for the match-up to materialise, before taking another dig at David Haye and calling on the former heavyweight champion to drop back down and take him on at cruiserweight.
"I've just beat the best cruiserweight in the world, I'm the best now I don't care what they all say," Bellew told Sky Sports.
"Denis Lebedev, I ain't coming to Russia, come and get this baby, because I've got the main belt now.
"I'm the man to beat in this division, come and get this.
"Or that b**** from Bermondsey (Haye), I'll fight him too, come back down to your natural weight and fight a real cruiserweight, because you've gone long enough fighting them clowns."
Bellew played 'Pretty' Ricky Conlan in Sylvester Stallone's film Creed, and insisted he had turned fantasy into reality by becoming a real-life world champion.
"I am Everton, and that's why I got up. Nothing was going to stop me tonight," said Bellew.
"I've achieved a dream tonight, all those people who said I couldn't do it, well I've done it. I'm world champion, that's what I am!
"The last time I saw something like that I was in a Hollywood movie, now it's real.
"I've lived the dream tonight. I am the best cruiserweight in the world, I have proven it tonight."
Bellew revealed he was beset by injuries during his pre-fight training camp, forced to spend time in an oxygen chamber in a bid to solve a rib problem.
"It was a disaster of a camp, I was in a hyperbaric chamber four weeks ago, I had a detached floating rib," said Bellew.
"I had a messed up left hand in camp as well.
"The only thing that went well was the rounds of sparring.
"But who cares, I made no excuses, I came here tonight as challenger, I leave as champion of the world."