He grew up in the High Sierra town of Sierra City, population 225. His father was a carpenter and stone mason, and his mother was a home-maker and a substitute teacher. Ostrom graduated from Roseville High School (California) in 1971, attended Sierra College in Rocklin (California), and earned a B.A. with honors in English at the University of California, Davis. At Davis, he went on to earn an M.A. and a Ph.D. in English, completing a dissertation on British Romantic Verse Satire in 1982 [DAI 44, no. 01A (1982): 0177.] While at Davis he took creative writing classes from Karl Shapiro (1913-2000), a Pulitzer-Prize-winning poet. In 1980-81 Ostrom was a Visiting Lecturer in American Studies at Johannes Gutenberg University of Mainz, Germany.

He joined the English Department at the University of Puget Sound in Tacoma, Washington, in 1983. He is Professor of English at Puget Sound, and he has served as co-director of African American Studies and Chair of the English Department.

Ostrom is author of A Langston Hughes Encyclopedia (Greenwood Publishers, 2002) and editor, with J. David Macey, of The Greenwood Encyclopedia of African American Literature, 5 volumes (Greenwood Publishers, 2005; he also contributed 37 entries to that encyclopeida. With Wendy Bishop (1953-2003), with whom he was a student at U.C. Davis, and Katharine Haake, he wrote the textbook Metro: Journeys in Writing Creatively (Longman, 2001).

Ostrom has been publishing poetry and short fiction in British and American magazines since the late 1970s. He is also author of the poetry chapbook, Subjects Apprehended (Pudding House Press, 2000), and The Coast Starlight: Collected Poems 1976-2006 appeared in 2006 (Indianapolis: Dog Ear Publishers). In 1992 he published a book of criticism about the short fiction of Harlem Renaissance writer Langston Hughes (1902-1967): Langston Hughes: A Study of the Short Fiction (Twayne, 1992). In 1990, Ostrom's detective novel, Three To Get Ready, was published by Cliffhanger Press in Oakland, California.

Ostrom was a Fulbright Senior Lecturer at Uppsala University in Sweden in 1994. Ostrom has published articles on British writers William Blake and George Meredith, and he contributed entries to the New Oxford Dictionary of National Biography. At the University of Puget Sound, he has taught courses in creative writing, literature, and rhetoric. He has also taught courses on detective fiction, the Harlem Renaissance, and contemporary American poetry. A recent novel by Ostrom is Honoring Juanita (2010).