Comprising 330,000 sq ft of space, the new leisure hall will be covered with a striking undulating glazed roof structure.
This will allow the developer to increase the entertainment and dining offerings to the shopping centre as it seeks to become an experience-led destination.
British Land said the expansion plan would also include a cinema to replace the existing one, a gym, and flexible leisure space which could be turned into an indoor golf or ten-pin bowling sites.
The extension is the next phase of Meadowhall’s evolution and will follow a £60m refurbishment which is underway and due to complete at the end of 2017.
Sheffield City Council is expected to make a decision on planning in spring 2017.
If the proposals are approved, British Land hopes to start on site during 2018 creating over 500 jobs during construction.
Charles Maudsley, Head of Retail and Leisure for British Land, said: “Understanding and anticipating our customers’ needs is a key strategic focus area and the Meadowhall Leisure Hall proposals respond to the changing way people live their lives.
“The exciting £60m refurbishment completing next year, the continued leasing success and Leisure Hall plans combined reinforce our commitment to ensuring Meadowhall remains an outstanding place for modern consumer lifestyles.”
Richard Wright, Executive Director of Sheffield Chamber of Commerce, said: “The Leisure Hall will be a jewel in the Sheffield City Region’s crown, set amongst other equally important investments in this great city.
“We therefore welcome British Land’s exciting plans and lend them our wholehearted support. They will reinvigorate Meadowhall and serve as a catalyst for further investment in the region.”