The Germans, who went unbeaten through the tournament and were appearing in their first final, broke clear of Serbia in the third quarter in Manila.
Serbia launched a furious fourth-quarter fightback but Germany managed to hold them off and put their name on the Naismith Trophy.
Dennis Schroder finished as Germany's top scorer with 28 points, followed by Franz Wagner with 19.
Germany had beaten the United States in a dramatic semi-final.
"We're the champions of the world, we're undefeated, we won every single game," said Germany's Maodo Lo.
"We had a tough group to begin with, we were able to keep building, we had huge wins throughout the whole tournament and then we faced the United States in the semi-final.
"I think we deserved this world championship."
Serbia, who were looking to win the title for the first time as an independent nation, lost small forward Ognjen Dobric to injury with less than three minutes of the game gone.
Dobric had to be carried off after a hard landing while attacking the basket.
He later reappeared at courtside, cycling on an exercise bike, but did not come back into the game.
Serbia were cheered on by a large group of travelling supporters but could not keep up with Germany in the second half.
"We made a great success," said Serbia's Aleksa Avramovic.
"Our heads are already up. Our next goal is to go to the Olympics... and make a better success than this."
Avramovic finished as Serbia's top scorer with 21 points, followed by Bogdan Bogdanovic with 17.
There was little to separate the two teams in a fiercely fought first half that ended 47-47.
That all changed in the third quarter when Germany outscored the Serbians 22-10.
Serbia came roaring back into the game in the fourth quarter, and cut the deficit to three points with less than a minute remaining.
A lay-up from Schroder helped steady Germany's nerves, and a missed three-point attempt from Avramovic ended Serbia's hopes.
"They deserved this win," said Serbia head coach Svetislav Pesic.
"They played 40 minutes at a high level, with continuity, very physical.
"If one team like Germany won all the games from the start until the end, we must everybody say bravo."
Serbia were playing without power forward Borisa Simanic, who underwent surgery to remove a kidney after getting injured earlier in the tournament.
They were also without superstar Nikola Jokic, who skipped the tournament to rest after leading the Denver Nuggets to the NBA title last season.
