Born and raised in Greece, Broumas secured a fellowship through the Fulbright program to study in the United States at the University of Pennsylvania; she earned her Bachelor's degree in architecture. She later went on to earn an MFA in creative writing from the University of Oregon. Broumas was selected by Stanley Kunitz for the Yale Younger Poets Series in 1977, the first non-native speaker of English to receive this award. Other honors have included a Guggenheim Fellowship and two fellowships from the National Endowment for the Arts. She has been Poet-in-Residence and Director of Creative Writing at Brandeis University since 1995. She lives on Cape Cod, where she, in the eighties, founded and taught at a school for female artists called Freehand, Inc.