All 25,000 seats for the four-night event in the grounds of Windsor Castle had been bought within five hours of going on sale at 09:00 GMT.
It will take place between May 12 and May 15 next year, with members of the Royal Family due to attend each night.
The Queen herself will attend a performance on the final evening, which will be broadcast live on ITV.
Singer Katherine Jenkins will be among 1,500 participants including musicians, dancers, famous actors and artists. The event will also feature 900 horses.
Tickets were priced from Â£55 to Â£195, with the most expensive seats situated next to the Royal Enclosure.
Some 5,000 free tickets will be available which will allow guests to see celebrities arriving on the red carpet. Details of how to apply will be announced in the new year.
The final night's show was the first to sell out. The Queen turns 90 on 21 April 2016.
A spokeswoman for the event organisers said: "They were selling very, very quickly. By 9.30am, 4,000 tickets had already been sold."
The celebration at Windsor is a not-for-profit event and aims to raise a surplus to donate to charities.
National commemorations will centre on her official birthday weekend in June with a mass street party in The Mall, a service of thanksgiving at St Paul's Cathedral and the traditional Trooping the Colour ceremony.
Tickets for a celebration to mark the Queen's 90th birthday sold out within hours of going on sale.