Kathleen Harkin was last seen on the banks of the river near Woody Island in the North Muirton area of Perth at around 9.30pm on Saturday.
A major land and air search involving police divers and a helicopter was launched, and a body was pulled from the river on Monday afternoon.
Police Scotland said it has now been formally identified as that of the missing Perth Grammar School pupil.
The force said there are no suspicious circumstances and a report will be submitted to the procurator fiscal.
Fellow pupils at the teenager’s school are being offered support by education and children’s services.
In a statement, police said: “Police Scotland can confirm that the body of a female who was recovered from the River Tay near St Madoes, Perthshire, has been formally identified.
“She has been named as 15-year-old Kathleen Harkin, from Perthshire.
“There are no suspicious circumstances and as with all sudden deaths, a report will be submitted to the procurator fiscal.”
Perthshire North MSP and Deputy First Minister John Swinney said: “My heart goes out to the family of Kathleen Harkin and to her friends at Perth Grammar School.
“The news today is heartbreaking and I cannot begin to imagine the devastation they will all feel. I have spoken to the headteacher at Perth Grammar and I know support is being provided for Kathleen’s school friends at school.
“I pray that Kathleen’s family and friends find peace at this desperately sad time.”