The devolution deals which leaders in West Yorkshire and the Sheffield City Region hope to complete this year are likely to give them the ability to set up the new organisations, which can draw on a wide range of powers to boost the economy and create jobs in specific areas.
The South Tees Development Corporation, which was set up in 2017, aims to create thousands of new jobs and add £1bn a year to the economy by regenerating 4,500 acres of land south of the River Tees.
This includes the former SSI Steelworks site between Middlesbrough and Redcar in the old North Riding of Yorkshire, which closed in 2015 with the loss of around 2,000 jobs.
Plans for a mayoral development corporation (MDC) were first announced in 2016 by former Deputy Prime Minister Lord Heseltine in 2016 in a bid to attract investment back to the site.
And since then a deal with the Thai company which owns SSI Steelworks has been struck, meaning the huge site is now in the hands of the recently-created public body.
Conservative metro mayor Ben Houchen, who chairs the South Tees Development Corporation (STDC), said the project had so far been a success.
He said the extra powers handed to an MDC, such as becoming the planning authority for the area instead of local councils, made the area more attractive for investors but had the potential to create political controversy.
He said: "If you've got a devolution deal, the combined authority should really be looking at economic growth, regeneration and job creation within a region anyway and in effect a development corporation is a subset of that.
"The reason we've only set up one is that you only really need them when you've got a substantial regeneration project that needs a more focused approach. In West Yorkshire and South Yorkshire the combined authority is going to do that work.
"Development corporations work when you have a very specific project that takes its own strategy, its own process, its own team that is spending all day every day tackling what is a complex specific challenge."
He warned that an MDC would need its structure with a board and chairman which could be considered "bureaucracy for bureaucracy's sake unless you can see that actually having its own organisation with its own set of powers can actually add value".
He said that for this reason there would be little reason to set up an MDC for an area like Leeds city centre as this would already fall within the remit of the West Yorkshire Combined Authority.
MDCs can draw on a wide range of powers, covering infrastructure, financial incentives, regeneration and land acquisition, devolving powers from central government to the local area.
Legislation allowing them to be created passed into law in 2011. The first was set up to regenerate the site of the 2012 London Olympics. So far, outside London, similar bodies have only been set up in South Tees and Stockport in Greater Manchester.
The West Yorkshire devolution deal signed last month, transferring powers and resources to a new metro mayor, allows them to designate a mayoral development area and set up an MDC.
But whether one is set up is likely to depend on whoever is elected metro mayor next year.
Both West Yorkshire and Sheffield City Region mayor Dan Jarvis could in theory set up more than one MDC each if they thought it necessary.