The decision led to acrimony as today's meeting broke up with the leaders of Barnsley and Sheffield councils in what appeared to be a heated exchange.
Sheffield Council leader Julie Dore also clashed with Doncaster Council chief executive Jo Miller.
Moments earlier, Barnsley and Doncaster had defied last-minute pressure from the Government and voted against plans to press ahead with the next stage of the deal in readiness for the election of a Sheffield City Region mayor in May.
The pair both voiced their continued support for the idea of an alternative wider One Yorkshire deal in partnership with 15 other Yorkshire councils despite two previous backers, Harrogate and North Yorkshire, expressing doubts over the weekend.
Sheffield and Rotherham continued to voice their support for the Sheffield City Region deal at a crunch meeting in Rotherham today.
As things stand, the outcome of today's meeting means a Sheffield City Region mayor election will still take place in May, but the mayor will have very few powers.
The decision also means South Yorkshire will not receive the Â£30m a year in extra funding agreed as part of the deal signed with then chancellor George Osborne two years ago.
Barnsley Council leader Sir Steve Houghton told the meeting "a lot's changed" since the deal was first signed including the decision of Chesterfield and Bassetlaw to pull out earlier this year.
He said his authority welcomed the emergence of the One Yorkshire plan, backed by 17 councils including his own, because of the scale it offered although he acknowledged the Government has yet to be convinced of the case.
"If that to some extent means we have to wait for that for a while we are prepared to do that because we feel the prize of a wider geography, particularly the Yorkshire geography, and the enthusiasm for that is a unique opportunity.
"I think our challenge across the region is to persuade (Local Government Secretary Sajid Javid) of the benefits that can be achieved by that," he said.
Communities Secretary Sajid Javid made a last-ditch attempt to save the Sheffield City Region deal on Friday with a letter which effectively ruled out the Government ever supporting One Yorkshire.
The letter amounted to a warning to Barnsley and Doncaster that if they voted down the Sheffield City Region deal they risked never benefiting from devolution agreements.
It appeared to succeed in shaking support for One Yorkshire over the weekend as Harrogate and North Yorkshire indicated they wanted to try and persue a devolution deal without Barnsley and Doncaster.
But the two South Yorkshire authorities today insisted they were committed to making One Yorkshire a reality.
Doncaster elected mayor Ros Jones said business in her district wanted to see a Yorkshire-wide devolution deal.
She said the Sheffield City Region deal without Chesterfield and Bassetlaw was "too small".
Sheffield City Council leader Julie Dore called for the deal to go-ahead arguing it would not stop a wider Yorkshire deal going ahead in the future.
She said risk of losing the benefits of the existing deal meant council leaders had a “duty” to press ahead.
Rotherham Council leader Chris Read described the collapse of the deal as “the latest failure of councils across our region to grasp the funding and opportunities already enjoyed by other parts of the country.”
Coun Read said the decision to scrap the deal “would almost inevitably mean fewer resources to bring more jobs to our local economy”.