An "in-principle" agreement was struck between council leaders and chancellor George Osborne in October.
Under the deal an elected mayor would take responsibility for transport budgets and strategic planning and have access to Â£900m of government money over the next 30 years.
The online consultation runs from 2 December to 15 January.
Sir Stephen Houghton, leader of Barnsley Council and chair of the Sheffield City Region Combined Authority, said: "We're asking residents and businesses to have their say on our proposed deal with Government.
"We know that business growth and better job opportunities are issues that people really care about and that's why we're encouraging as many people as possible to take part."
The city region is comprised of the nine local authority areas of Barnsley, Bassetlaw, Bolsover, Chesterfield, Derbyshire Dales, Doncaster, North East Derbyshire, Rotherham and Sheffield.
The leaders of all nine councils must formally approve the deal.
A six-week consultation on a proposed devolution deal for the Sheffield City Region has begun.