The 79-year-old chart-topper has added a second concert on Monday 10 August after every ticket was snapped up for his show at the Ross Bandstand two days earlier.
Promoters DF Concerts have confirmed eight shows so far for their Summer Sessions series, which Sir Tom will launch.
Now in its third year at the open-air venue, which the promoters describe as "the perfect destination for music fans," the series of concerts is expected to run from 8-20 August.
Sir Tom was the first ever act to play the Summer Sessions series when it was launched two years ago.
Also confirmed for Princes Street Gardens gigs so far this year are Lionel Richie, Michael Kiwanuka, The 1975, McFly, Simple Minds and Travis.
The gigs, which have a capacity of up to 6000, were announced last month as a city council report estimated the previous year's shows to be worth £5.5 million to the economy.
More than 47,000 fans flocked to shows by the likes of Lewis Capaldi, Primal Scream, Chvrches and Madness last year, with 36 per cent of tickets snapped up by local residents.
A spokeswoman for DF Concerts said: "One of the most influential showmen in music, the Welshman is clearly in high demand, as he promises non-stop entertainment for fans in the picturesque setting of Princes Street Gardens.
"Bringing timeless classics like ‘It’s Not Unusual’ and ‘Sex Bomb’ to the stage, Tom Jones is an Edinburgh Summer Sessions favourite and these look set to be two unforgettable shows."