The E20 Stadium Partnership, which manages the site, says the new roof will turn the stadium into a multi-use venue.
Dismantling the existing roof will start later this year, and the new one - twice as big and covering every seat in the ground - will be built and lifted into position.
The new roof is due to be completed by spring 2015, in time for the rugby World Cup.
Other work to transform the stadium will be finished a year later, ahead of the 2016-17 football season, when it will become home to West Ham. Retractable seating will allow for pitch-side viewing at football matches.