Rayson was born in Melbourne, Victoria and graduated from the University of Melbourne and the Victorian College of Arts. She has worked as a freelance journalist and editor in addition to her primary career as playwright and screenwriter. Rayson was the co-founder of the community theatre group, Theatreworks in Melbourne's eastern suburb of St. Kilda, working there for four years while writing. Rayson has been writer-in-residence at Geelong's Mill Theatre, Playbox Theatre, La Trobe University (which has awarded her an Honorary Doctorate of Letters), and Monash University.

Recognised as one of Australia's most significant playwrights, Rayson's first major success was Hotel Sorrento, which won several prizes including the Australian Writers Guild Award. The play has become an Australian classic, regularly performed by regional theatre groups, and appearing in university courses and on the high school syllabus. The film of the play, directed by Richard Franklin, won an AFI Award for best screenplay (Peter Fitzpatrick and Franklin). In 2010, the play's London debut won critical acclaim.

New Rayson plays have been a popular mainstay of Australian state theatre companies' programming for the past decade. Her more recent works are Falling from Grace, Scenes from a Separation (written with Andrew Bovell), Competitive Tenderness, Life After George, Inheritance, The Glass Soldier and The Swimming Club.

Rayson's commitment to plays that engage with social issues was most evident in her 2005 work Two Brothers, an attack on the hardline asylum seeker policy of Australia's conservative Howard government. The play provoked bitter controversy, especially from people who saw its central character, a ruthless politician, as a cruel parody of Australia's deputy prime minister, Peter Costello. Rayson claimed that Costello, who had played no part in asylum seeker policy, was not her target: she was satirising the government as a whole, and exploring the phenomenon of the family rent by political division.

Rayson was the joint recipient of the Sidney Myer Performing Arts Award in 1996 and has won Victorian and NSW Premier's Literary Awards and three prestigious Helpmann awards. She is the only playwright ever to be nominated for the Miles Franklin Award.

Her TV writing credits include SeaChange.