Anne Brookman was born in Port Broughton but grew up in Victor Harbor, South Australia. She studied to be a pre-school teacher and taught for about 12 years. She lived in the UK from 1971 to 1975 and later returned South Australia, living on a farm at Currency Creek, raising beef cattle and making furniture.
Brookman's first play, 'Mr Rumble's Jumble', was performed at Come Out, 1979. After that, she wrote or co -wrote over 20 plays, many of which have been produced by professional theatre companies in South Australia including Troupe, Vitalstatistix, Patch, Junction and the Adelaide Festival Centre Trust.
Brookman has written scripts for children's television programs for Thames Television, Channel 7, Channel 9 and the ABC. In 1991 she received a fellowship from the Literature Board of the Australia Council, and in 1992 she received the Carclew Fellowship, the Adelaide Festival award for writing for young people.