Plans to hold a community poll were announced by Barnsley and Doncaster councils earlier this month.
Voters would be asked to choose between the government-backed Sheffield City Region deal or a proposed Yorkshire-wide deal.
The Yorkshire Post says: Why devolution to the North can’t be delayed any longerAt a full council meeting of Barnsley Metropolitan Borough Council, every councillor voted for the poll to go ahead. Doncaster councillors will be asked to back a separate vote later today.
When the move was announced, Barnsley Council leader Sir Steve Houghton said while the result of the poll would not be legally binding, he wanted to give Barnsley residents an opportunity to have their say on "a generation-changing decision on devolution".
According to council documents, holding the poll would cost each authority £120,000. Votes would be cast either by post or online, with a closing date of December 20. The result will be announced on December 21.
South Yorkshire's ongoing devolution saga which began in 2015 when the-then Chancellor George Osborne signed an agreement with Sheffield City Region leaders, which includes Barnsley, Doncaster, Rotherham and Sheffield.
Under the deal a directly elected mayor, due to be elected in May 2018, will be given £900m over 30 years and handed power over transport budgets and strategic planning.
But, in August, the leaders of Doncaster and Barnsley signed up to a pan-Yorkshire proposal, initially backed by 17 of the 20 local authorities in Yorkshire.
Sheffield and Rotherham Councils have not given their support to the deal and the Department for Communities and Local Government says it is not prepared to consider any proposal that cuts across the Sheffield City Region deal.