Most events and venues went ahead with full houses and socially distanced audiences after the lifting of restrictions was delayed until August 9.
Sell-outs have been reported across the festivals since the first tickets went on sale in June, due to the limited capacity of venues and reduced number of performances this year.
The bulk of the tickets sold were for Fringe shows, with venues reporting an overall audience of around 400,000 at the latest count.
Nearly half of the Fringe’s ticket sales were generated outwith Scotland, with well over a third drawn from Edinburgh and 17 per cent from the rest of Scotland.
The Edinburgh International Festival, which staged all of its shows with two metre distancing enforced, based on the restriction in place when tickets went on sale, said it sold 51,000 tickets for its programme, which was largely staged across three outdoor sites.
More than 60 per cent of its tickets were sold in Edinburgh, while a further 350,000 watched shows for free online around the world.
The Edinburgh International Book Festival said it had sold 56,000 in person and online tickets, with total footfall of 25,000 being recorded at its new home at the Edinburgh College of Art.
The Edinburgh International Film Festival said 12,000 people had attended its events at the Filmhouse, St Andrew Square and at the Festival Theatre.
Fringe Society chief executive Shona McCarthy said: “When registration opened in May, we had no way of knowing for sure what this summer would look like.
“Today we celebrate every single show that has been brought to life.
“We’ve still got work to do to ensure the Fringe recovers – but recovery isn’t about growth in the statistical sense. It’s about growth as a Fringe community.”
Fergus Linehan, director of the Edinburgh International Festival, said: “The success of the festival can be measured in the joy of audiences attending live performance once again, artists returning to the stage and giving exceptional performances in unfamiliar settings, the seamless experience of our outdoor venues, our beloved theatres opening their doors once more and the engagement of communities right across the city.
“We even enjoyed good weather that added to the collective delight and good humour that seemed to pervade every performance.
"We salute our sister festivals for their innovation and creativity. Together we hope we gave Edinburgh a festival season to remember.”
Book festival director Nick Barley said: “This year was a year of transition and experimentation.
"I am extraordinarily proud of the team that has conceived, programmed and delivered a festival under the restrictions and uncertainty that we experienced right up until the beginning of August.
“We were at the very forefront of live events coming back, and there was understandably a nervousness amongst many of our regular audience in coming together in the same space. As the festival went on we saw visitors, and confidence, growing.”
Film festival chief executive Ken Hay said: “We are absolutely delighted that audiences came together with us in cinemas across Scotland, outdoors and online to enjoy an exciting, diverse and accessible festival this year.”