Bosse made an astonishing switch of pace with 160m to go, to pass Kenya's Kipyegon Bett and Nijel Amos.
Coming into a home straight Bosse had opened a gap of severa meters alongside with race favourite Amos of Botswana.
Poland's Adam Kszczot came very hard from the back to close the gap between himself and Bossse, but the Frenchman managed hold off the Polish athlete to claim the World championships gold in a new season's best time of 1:44.67.
"I live a dream, I'm in a dream right now, am I dreaming?" said Bosse.
Kszczot won the silver medal in a new season's best 1:44.95 as Kipyegon Bett of Kenya settled for third in 1:45.21.
1 Pierre-Ambroise BOSSE FRA 1:44.67 SB
2 Adam KSZCZOT POL 1:44.95 SB
3 Kipyegon BETT KEN 1:45.21
4 Kyle LANGFORD GBR 1:45.25 PB
5 Nijel AMOS BOT 1:45.83
6 Mohammed AMAN ETH 1:46.06
7 Thiago ANDRÈ BRA 1:46.30
8 Brandon MCBRIDE CAN 1:47.09