Kevin McCoy said costs on the $250-million design phase of the ships is between $20 million and $30 million under budget.
The final numbers are expected at the end of next year.
McCoy said most of the design is complete and construction of the vessels is still scheduled to begin next September.
The federal government has said it plans to build six to eight of the ships, but the auditor general has warned the navy may not get the type or number of vessels it needs because of cost restrictions.
The shipyard held an event Wednesday to mark the installation of the last piece of structural steel to the production building where the ships are to be built.Suggest a correction