The 16 million project to replace the grandstands is due to be completed next summer.
Tattoo chief executive and producer, Major General Euan Loudon, said: "I am delighted to advise that the Tattoo's new stands project is on time and on budget and we are confident that it will be in place for opening night on August 5."
The new stands will offer more leg room for spectators, improved disabled access, and better rest areas for performers.
The project will also reduce the time it takes to put the stands up and down. The existing stands are 36 years old and were based on the system used for the 1972 Munich Olympics.
Tickets for next year's Tattoo go on sale on December 1.