He took his 10th podium of the season and an unbeatable lead over New Zealanders Nick Cassidy (28) and race-winner Mitch Evans (29) for Envision Racing and Jaguar respectively.
Dennis now has 213 points to Evans's 176 and Cassidy on 174.
"To become world champion is mind-blowing," said Dennis, who was third at the finish but moved up to second when Porsche's Antonio Felix da Costa (31) was penalised.
"I really didn't think it could happen coming into this year."
Cassidy started on pole position as Dennis's closest rival, 24 points behind with Evans a further 20 adrift, but retired after contact with teammate Sebastien Buemi (34) in a race that was twice red-flagged.
The title was US team Andretti's first in Formula E.
"It was insane, I think that basically explains what Formula E is all about," said owner Michael Andretti. "You just never know all the way until the last lap. Even those last two laps we were just holding our breath.
"I can't thank the team enough, hanging in there all these years to finally get on top of a podium for the championship."
Formula E's first season was in 2014-15 and Dennis is the eighth driver to take the title with France's Jean-Eric Vergne (33) the only double champion.
Brazil has had two champions while the others up to now have come from Switzerland, France, Portugal, the Netherlands and Belgium.
The teams' championship will go down to Sunday's finale at the ExCeL Centre with Envision Racing and powertrain provider Jaguar level on points. Porsche also still have a mathematical chance.
