Proposals for the eight-team tournament, designed to rival similar events such as the Indian Premier League and Australia's Big Bash, were approved by 38 of the ECB's 41 members.
Essex and Middlesex were the only two English counties who voted against the plans, while Kent abstained.
"We are delighted that such an overwhelming majority of our members have voted to support the change to the ECB's Articles," said ECB chairman Colin Graves in a press release.
The new tournament will sit alongside England's existing domestic competitions, including the T20 Blast.
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The cities that will host teams have not yet been announced.
"Over the past year our members have seen the clear evidence outlining why an additional new T20 competition is the right way for cricket to reach new audiences, create new fans and drive the future of the game," Graves added.
"I passionately believe that the game has chosen the right path. Each of our members will benefit and, critically, so will the whole game.
"The benefits it will bring can deliver a sustainable future for all 18 first-class counties and an exciting future for the game in England and Wales.