The 21-year-old from Wiltshire needed to finish 14th in Spain to secure the title and began 18th on the grid.
He finished ninth on his Honda, with race winner Miguel Oliveira of Portugal second in the final standings.
Barry Sheene was the last British champion, winning the 500cc in 1977.
Kent won five of the first nine races of the season, but two retirements and a highest finish of sixth in the last five events saw his commanding lead reduced to 24 points going into the final weekend.
Oliveira's third successive victory was his sixth of the season, matching Kent's tally of wins, and the pair will be team-mates in Moto2 next season.
"The emotions are so high, in the last four races there was a slight chance of being world champion and it's normal to be disappointed each time but for sure we are going to have a great evening," Kent said.
"It's an amazing feeling, a dream come true. You need luck, a great bike and a great team behind you."
Danny Kent became the first British motorcycling Grand Prix champion for 38 years as he sealed the Moto3 Championship by six points in the final race in Valencia.