County chairman Stephen Taylor revealed that they took their decision following a vote by the club's board.
Each county is guaranteed revenue of £1.3m from the competition, which is planned to get under way in 2020.
The only two counties who have so far not backed the ECB proposal are Essex and Middlesex.
"The new competition will provide much-needed revenue to all clubs," said Taylor. "With significant additional investment in recreational cricket - something we are very keen to develop.
"The preservation of all formats of cricket at New Road is fundamentally important. This will go a long way to protecting the four-day game, 50-over competition's and the T20 Blast."
The changes require the support of 31 out of 41 of the ECB's voting members, which comprise the 18 first-class counties, 21 recreational boards, the Minor Counties Cricket Association, and the MCC - owners of Lord's and Middlesex's landlord.
A number of counties have come out in support of the proposals for the new tournament.
Derbyshire, Leicestershire, Somerset, Sussex, Yorkshire and Durham have all announced that they will back the ECB rule change, while Kent have abstaned.
Others, including Glamorgan, Hampshire and Warwickshire - the only county who already play their T20 cricket under a city banner as Birmingham Bears - have been vocal in their support for a city-based competition, while Surrey director of cricket Alec Stewart has expressed concern over the details of the new event.
Worcestershire have become the latest county to back the England and Wales Cricket Board's proposed new eight-team city-based T20 competition.