According to the paper, the gift is the single biggest bequest in the festival's history.
The proceeds for Scully's donation came from the sale of two adjacent houses in Dublin, property that was left over from her estate after gifts to friends. She specified in her will that the money be used for promoting the careers of young artists.
Edinburgh International Festival director Brian McMaster told The Scotsman, "It's fantastic, it's absolutely wonderful and it's something concrete that she will be remembered by. She's doing something great, something for the Festival, the thing she cared most about."
Scully worked in agricultural public relations and donated just Ô£45 a year to the EIF while she was alive, according to the paper, but frequently spoke of giving more in her will.
The legacy is being used for the first time this year, helping to pay for pianist Llyr Williams's appearance with the Minnesota Orchestra and a performance of Schumann's Manfred which features several young artists and singers performing with the BBC Scottish Symphony Orchestra.
The Edinburgh International Festival opened on Sunday night (August 13) with a concert performance of Strauss's Elektra at Usher Hall.