An £8 million improvement programme proposed by the local authority's city centre management company would see the area opened to the public with a series of natural stone walkways.
Grassed areas and lighting would also be introduced along with a continental-style coffee bar. Musical performances would be staged in the square, along with one-off live events.
"We are well aware of the responsibility attached to reworking a space in Edinburgh's New Town," said Professor Brian Evans, a partner at architectural firm Gillespies, which has drawn up the project.
"The design will recover the distinctive qualities of the square, which have been eroded over time, while introducing appropriate, subtle features such as a small, elegant pavilion."
It is anticipated that plans for the scheme will be lodged with the city council in the next few weeks. Work could be completed by the end of 2006.
City centre manager Ian Broadfoot said: "The redevelopment of St Andrew Square and its opening to the public will create a space in Edinburgh city centre to rival the finest examples from around the world."