First Minister John Swinney said Ross’s family would be supported by the Scottish government and the Foreign and Commonwealth Office.
He said: “This is an absolutely appalling case that has been reported overnight.
“And obviously I’m deeply concerned that such a tragedy has taken place.”
Helena Smith, The Guardian’s correspondent in Athens, told Radio Scotland that the body was found in a derelict building in downtown Athens, “in an area that is booming, full of Airbnbs”.
She said: “It is very popular with people travelling through Athens and young foreigners who have elected to make the Greek capital their home.”
Smith said that Ross had family in Edinburgh and “connections” to Greece – staying with a friend in Athens before she disappeared.
She added: “It would seem that someone had control over her mobile phone after she died and was sending messages to distract the authorities and close friends from trying to track her down.”