The proposed "Leisure Hall" development will include a new cinema, restaurants, bowling and indoor golf.
Joint owners British Land said the new 330,000 sq ft (27,800 sq m) facility was a "significant" step in improving the centre's "leisure provision".
A planning application is due to be submitted this year.
British Land said the proposal will mean Meadowhall can provide "dining and entertainment experiences not currently available at the centre".
Centre director Darren Pearce said the extension will be housed beneath a glazed, lattice roof "four times the size" of the roof at King's Cross railway station.
"This is a very exciting era for Meadowhall," he said.
"This is more than it cost to build Meadowhall in the first place so it's a massive commitment by investors to the region."
A public consultation is due to be held on 3 and 4 June at the shopping centre.
If the plans are approved work on the new leisure hall is expected to begin in 2018 with a view to opening in late 2020.
Meadowhall opened in 1990 at a cost of £250m.
Last year, British Land announced it was investing £50m in refurbishing areas of the existing site. It co-owns the site with Norwegian investment fund, Norges.
Plans for a £300m extension at Meadowhall shopping centre - creating more than 1,000 jobs - have been revealed.