The 23-year-old Ireland team captain beat Murodjon Akhmadaliev of Uzbekistan on a unanimous points decision in Doha.
Conlan shaded the first round and clearly took the second but had to hang on at the end after being knocked down in the final minute.
He adds the world crown to his European and Commonwealth titles.
Conlan had already qualified for next year's Olympic Games in Rio.
"I am a bit embarrassed at getting knocked down in the last round," said Conlan.
"It is the first time I have been on the canvas in my life. He hit me sweet on the chin and it was the best punch I have ever been hit with.
"But I recovered really quickly and I am really happy."
Irish light-heavyweight Joe Ward is also through to the final at the World Championships and fights Julio La Cruz of Cuba on Thursday evening.
Earlier, Michael O'Reilly lost a controversial decision to Hosam Abdin of Egypt in their box-off for a place at the Olympics.
Belfast's Michael Conlan has become the first Irish male to win a senior World Amateur Championship title with victory in Wednesday's bantamweight final.