Gergiev, who became artistic director in 1988, has been ambitious in expanding beyond the original Mariinsky. A second theatre concert hall with 1,200 seats opened in 2007.
The New Mariinsky opera house will be directly across the canal from the original building.
Russia annulled the initial 2003 contract for the project given to French architect Dominique Perrault because of mounting costs and the impracticality of the design.
A new design competition was launched earlier this year.
"The biggest advantage of the project over that of Dominique Perrault is that it is without doubt realizable," Gergiev said in an interview with Agence France-Presse.
The projected date of completion is 2011.
Diamond + Schmitt is also known for its work on the Banff Centre for the Arts and recently won the contract for Montreal's concert hall.