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The competition is set to start in 2020 and will involve eight new city-based teams playing 36 games in 38 days.
"Cricket needs that moment in this country that changes the way we talk and think about it," said Vaughan.
He also said that he believes the ECB's aim for "significant" free-to-air coverage is key to the proposal.
ECB chief executive Tom Harrison called free-to-air ambitions an "aspiration which reaches at the heart of our proposition going forward".
He hopes the new competition will rival the Indian Premier League and Big Bash in Australia as the leading T20 tournaments in the world.
The Big Bash draws average crowds of more than 28,000 whereas Vaughan labelled the attendance of the current T20 Blast competition in the English county game as "nothing better than division three football".
"Everyone can see every ball of the Big Bash," said Vaughan, who was speaking on his BBC Radio 5 live show with ex-England spinner Phil Tufnell. "Cricket is there for everyone to see. I love the thought and talk of terrestrial partners and the game seen.
"But I don't think that is the be-all and end-all. I think it is important, but I think cricket has to do so much more.
"The only thing in terms of a county perspective is this new tournament will be a massive juggernaut, get loads of marketing and the county game may say: 'Why didn't we get that support?'
"Would the Blast have had more success if there was a terrestrial partner in play or had that kind of support? I guess the answer is yes."
He added: "I think the white ball game, in particular, and T20 is exactly the brand of cricket required to expand the game."
Current England captain Joe Root believes the plans for the new competition are a "good idea" and that "it is very important the public are given an opportunity to see cricket at a national level, on free-to-air TV".
Speaking on BBC Radio 5 live, the Yorkshireman added: "It will be interesting to see how things pan out and what decisions are made."
Squads of the eight T20 teams will be made up of 15 players and include three overseas players.
That will leave 96 players being selected from the 18 counties, which averages out at just over five apiece.
"If you picked 96 players out of county cricket now, the standard is remarkable," said Vaughan.
"Pick five-and-a-half players from each county and you add in the world-class overseas stars and you are going to get some terrific teams."
Vaughan played down concerns over fans not wanting to support certain city-based teams because of their county allegiance.
"Supporters will say I won't support Leeds or Manchester but I don't think they're going to be called the towns," said Vaughan who also addressed worries about the weather and the tournament being played when families travel abroad during the lengthy school summer holidays.
"The weather is nonsense because we might as well say 'we're not going to play because it might rain so let's cancel all cricket'," he said.
"In terms of holidays, the programme is six weeks long and I don't know anybody who goes away for six weeks. They might go for two weeks and they don't all go at the same time.  Again, that is nonsense."
Following a period of consultation, the ECB highlighted a "focus on recruiting the next generation of fans, in particular promoting attendance to a diverse, young, family audience".
"Where the Big Bash has had huge success is they made sure the fan experience is key," said Vaughan. "The cricket was almost secondary.
"It's around 50/50 of men and women in the crowd which is remarkable.
"They go back the week after because all the kids and all the families had a terrific night out."
On Monday, the ECB presented a detailed overview of its proposals for a new Twenty20 competition to its 41 members. These included:
A referendum is expected to be dispatched on Tuesday inviting stakeholders to sanction a tournament including eight teams, rather than the 18 counties who traditionally contest the main competitions domestically.
The ECB is made up of 41 stakeholders, which includes the 18 first-class counties, the MCC, the Minor Counties Cricket Association and the recreational boards, and a minimum of 31 will need to vote in favour for the plans to progress.
"I will ask the ECB board to trigger a change in our Articles of Association to enable the introduction of the proposed new T20 competition," said ECB chairman Colin Graves.
"We face a ground-breaking opportunity in the weeks and months ahead - and if our members embrace it, the ECB will work with everyone in the game to ensure this huge potential and the investment that will come with this delivers an even stronger future for the game."
A new Twenty20 tournament planned by the England and Wales Cricket Board "will be a roaring success", says former England captain Michael Vaughan.