Dubbed Deep Time, the event, soundtracked by Glasgow post-rock band Mogwai, saw the landmark used as a canvas for animated projections taking in 350 million years of history.
A planned live stream of the event malfunctioned, but spectators hailed the event as an "amazing spectacle".
The festival runs until 29 August.
A viewing arena was created on Castle Terrace for the show, which marked the start of Standard Life's three-year sponsorship of the Edinburgh International Festival.
On social media, Press Association reporter Ben Phillip described the event as "absolutely spectacular", while Joanna Keating said it was an "amazing spectacle" which "kicked off the festival in style".
The festival's organisers apologised for the failure of the live stream, but said a video of the event would be uploaded afterwards.
Deep Time was developed by the company 59 Productions with academics from Edinburgh University and will also look at the work of renowned Edinburgh scientist James Hutton (1726-1797), often referred to as the father of geology.
Leo Warner, creative director of 59 Productions, said: "Deep Time gives us an opportunity to build on the success of The Harmonium Project and to create a spectacular event that is more deeply connected to the story of the city."
Festival director Fergus Linehan said organisers wanted to "offer the people of Edinburgh and beyond a spectacular start to the summer festival season".
A spectacular light display on the side of Edinburgh Castle has marked the opening of the city's International Festival.