The Edmonton skip, who teamed with Evan Asmussen and twins Landon and Bryce Bucholz, sealed the victory with a five-point seventh end.
"It feels just amazing to be world champion," Bottcher said. "We've been curling all our lives to have a chance at something like this, and it's amazing to have gotten here and amazing to win it."
The Canadians opened with a single point in the first end and added pairs in the third and fifth ends.
Swedish skip Rasmus Wrana kept things close, scoring a single in the sixth end to cut the lead to 5-3. But Bottcher broke the game open in the seventh.
Sweden was in position to steal with a rock buried behind Canadian cover, but Bottcher followed with a tapout to score five and put things out of reach.
"My team set up the seventh end great," Bottcher said. "(Wrana) didn't have a whole lot and he was just a hair heavy on his last one and left me a shot, and I was fortunate enough to make it."
Both teams threw most of the eighth-end rocks through the house so that they could play out the obligatory number of ends. Wrana drew for one with the last rock and the teams shook hands.
"I think we were outplaying them just a little bit," Bottcher said. "We were ahead on the scoreboard and then in the seventh end we got it done, so that was good."
Parker Konschuh served as the fifth player on the Canadian team, which was coached by Bernie Panich.
It was Canada's first world junior men's title since 2007. Bottcher gave credit to his teammates for the achievement.
"This team has been amazing and they've made my job easy," he said. "This means that a lot of work we've put in this year and in years past has paid off for us."
Scotland defeated Norway 7-3 for the bronze medal.
In women's play, Scotland successfully defended its title with a 6-5 win over the Czech Republic while Russia beat Sweden 7-4 for the bronze.
Jocelyn Peterman of Red Deer, Alta., finished in sixth place.
Note to readers: This is a corrected story. A previous version had an incorrect year for Canada's last title win.