A £30m-a-year Sheffield City Region devolution was deadlocked after Barnsley and Doncaster councils pulled out, meaning metro mayor Dan Jarvis could not take control of the funding.
But Communities Secretary James Brokenshire, in a letter to political leaders, said it can proceed even if the two breakaway councils decide to leave at the end of the current mayoral term in 2022.
Councils who do not remain could then pursue a county-wide devolution deal, although the Government previously said the so-called One Yorkshire plan - favoured by political leaders in the region - does not fit the criteria.
Sheffield City Region mayor Mr Jarvis said: “This is a positive response from the Secretary of State and represents an important step towards the devolution of further powers and resources to communities across our region. It is however, important to remember that devolution is a process, not an event.
“The Secretary of State’s letter provides the basis for further dialogue, with leaders locally and nationally and the opportunity to make further progress.”
Mr Jarvis added: “Pragmatism, compromise, and a commitment to do the best for the people we represent will continue to be required on all sides.”
In March, South Yorkshire leaders reached an agreement where the two breakaway councils could rejoin the devolution deal until 2022.
The leaders of Doncaster and Barnsley councils were previously unwilling to support the arrangement if it did not allow them to pursue a Yorkshire-wide devolution deal.
In the House of Lords, Lord Bourne said Ministers “are ready to progress their deal along the lines they have proposed and, recognising the strength of the Yorkshire identity, to consider a localist approach to devolution elsewhere across Yorkshire”.
The development has raised hopes Yorkshire will get more control over funding and decision-making after years of deadlock.
In a statement, the council leaders backing One Yorkshire said: “We welcome the Government’s positive response to the constructive approach for unlocking the Sheffield City Region devolution deal set out by South Yorkshire leaders in their March letter and therefore the opportunity to progress One Yorkshire devolution discussions.
“We will continue to work with Ministers and their officials to agree a settlement ensuring all parts of Yorkshire can benefit from devolution and to ensure appropriate interim arrangements are put in place to support our region’s economic ambitions.”
The Government has said a One Yorkshire plan - where a single mayoral authority is created for the region of 5.2m - is too diverse. Northern Powerhouse Minister Jake Berry suggested earlier this year that he might consider smaller “city region” deals in Yorkshire.