Kaitlyn Vasconcellos, 24, was found after police were called to the Agnes Blackadder Hall in the Fife town on Tuesday.
Officers said the death was "not suspicious".
University Principal Louise Richardson paid tribute to the student who came from Rocklin, California, and was in her final year of an economics degree.
She said her death was "an unimaginable shock to her family in the USA and her friends and classmates here in St Andrews".
She said: "Kate had just given her final Honours presentation last Friday. I know that her teachers have been shocked and enormously saddened by her death.
"They will remember Kate as a quiet, thoughtful and determined student with an unfailingly pleasant nature."
The principal added: "She brimmed with energy and immersed herself in her studies and extra-curricular pursuits in St Andrews. Her passion was musical theatre. She was a member of the Gilbert and Sullivan Society and served on its committee.
"She had very loyal friends.
"Our student community has responded to this tragic news with characteristic compassion, and concern."
Dr Richardson said Ms Vasconcellos' parents had flown to Scotland this week, adding that it "really saddened her" to have to make the announcement.
A student who was about to graduate has been found dead in her room at St Andrew's University.