The proposed Leisure Hall at the South Yorkshire centre would create up to 1,400 jobs.
The 330,000 sq ft (27,800 sq m) facility would include a new cinema, restaurants, gym and new community spaces.
Joint owner British Land said the extension would "continue Meadowhall's evolution".
The plans, part of a five-year vision to extend the leisure offer at Meadowhall, include:
Around 540 jobs would be created during construction, in addition to 1,400 new jobs once the leisure hall is complete.
Sheffield City Council is expected to make a decision on the application in spring.
Darren Pearce, Meadowhall centre director and president of Sheffield Chamber of Commerce, said the extension would be a "major milestone" for the shopping centre.
Richard Wright, Sheffield Chamber of Commerce executive director, said it would be a "jewel in the Sheffield City Region's crown".
He added: "The Leisure Hall will retain spend in Sheffield city region by ensuring residents do not need to travel out of the area to fulfil their shopping and leisure needs.
"We welcome British Land's exciting plans and lend our wholehearted support.
"They will reinvigorate Meadowhall and serve as a catalyst for further investment in the region."
In Sheffield city centre, the current demolition of the Grosvenor House Hotel is under way.
It will be replaced by a new £90m HSBC building in the new year as part of the  Sheffield Retail Quarter.
A new city centre Primark store recently opened and a nine-screen cinema is due to open in the near future.
Detailed plans have been submitted for a £300m extension of Sheffield's Meadowhall shopping centre.